Fluid dynamics

On the Motion of a Sphere in a Viscous Fluid.323 perhaps never completely, oxidized by air at the ordinary temperature, and therefore when old coal-bearing strata are washed away, the bulk of the old carbonaceous matter may still help to increase the percentage in the new deposits.However~ even if we should have to make a liberal a]lowance for the destruction of old carbonaceous matter by oxidation in some way or other, the results obtained by this line of inquiry are not unfavourable to the credibility of a high estimate of the world's supply of fuel~ for all the elements in the above calculation, required to give us 500,000,000,000,000 tons of coal, viz.(1) the amount of rock annually denuded and again deposited (85,000,000,000 tens)~ (2) the length of time that this denudation has "been going on ('20,000,000 years), and (3) the proportion of organic matter present (0"03 per cent.), are more likely, taken as a whole, to err on the side of being estimated too low than of being estimated too high.[To be continued.] XXXI. ~7~e ~]/[otion of a Sphe~v in a Viscous Fluid~

@article{doi10108014786440009463920,
    author = "ALLEN, H. S.",
    title = "XXXI. The motion of a sphere in a viscous fluid",
    year = "1900",
    journal = "The London Edinburgh and Dublin Philosophical Magazine and Journal of Science",
    abstract = {On the Motion of a Sphere in a Viscous Fluid.323 perhaps never completely, oxidized by air at the ordinary temperature, and therefore when old coal-bearing strata are washed away, the bulk of the old carbonaceous matter may still help to increase the percentage in the new deposits.However\textasciitilde\ even if we should have to make a liberal a]lowance for the destruction of old carbonaceous matter by oxidation in some way or other, the results obtained by this line of inquiry are not unfavourable to the credibility of a high estimate of the world's supply of fuel\textasciitilde\ for all the elements in the above calculation, required to give us 500,000,000,000,000 tons of coal, viz.(1) the amount of rock annually denuded and again deposited (85,000,000,000 tens)\textasciitilde\ (2) the length of time that this denudation has "been going on ('20,000,000 years), and (3) the proportion of organic matter present (0"03 per cent.), are more likely, taken as a whole, to err on the side of being estimated too low than of being estimated too high.[To be continued.] XXXI. \textasciitilde 7\textasciitilde e \textasciitilde ]/[otion of a Sphe\textasciitilde v in a Viscous Fluid\textasciitilde},
    url = "https://doi.org/10.1080/14786440009463920",
    doi = "10.1080/14786440009463920",
    openalex = "W2073246117"
}

Penetration of Liquids into Cylindrical Capillaries.---The rate of penetration into a small capillary of radius $r$ is shown to be: $\frac{\mathrm{dl}}{\mathrm{dt}}=\frac{P({r}^{2}+4\ensuremath{\epsilon}r)}{8\ensuremath{\eta}l}$, where $P$ is the driving pressure, $\ensuremath{\epsilon}$ the coefficient of slip and $\ensuremath{\eta}$ the viscosity. By integrating this expression, the distance penetrated by a liquid flowing under capillary pressure alone into a horizontal capillary or one with small internal surface is found to be the square root of ($\frac{\ensuremath{\gamma}\mathrm{rt}\ifmmode\cdot\else\textperiodcentered\fi{}cos\ensuremath{\theta}}{2\ensuremath{\eta}}$), where $\ensuremath{\gamma}$ is the surface tension and $\ensuremath{\theta}$ the angle of contact. The quantity ($\frac{\ensuremath{\gamma}cos\ensuremath{\theta}}{2\ensuremath{\eta}}$) is called the coefficient of penetrance or the penetrativity of the liquid.Penetration of Liquids into a Porous Body.---(1) Theory. If a porous body behaves as an assemblage of very small cylindrical capillaries, the volume which penetrates in a time $t$ would be proportional to the square root of ($\frac{\ensuremath{\gamma}t}{\ensuremath{\eta}}$). (2) Experiments with mercury, water and other liquids completely verify the theoretical deductions.Dynamic capillary method of measuring surface tension is described. It possesses certain advantages on the static method of capillary rise.

@article{doi101103physrev17273,
    author = "Washburn, Edward W.",
    title = "The Dynamics of Capillary Flow",
    year = "1921",
    journal = "Physical Review",
    abstract = "Penetration of Liquids into Cylindrical Capillaries.---The rate of penetration into a small capillary of radius $r$ is shown to be: $\frac{\mathrm{dl}}{\mathrm{dt}}=\frac{P({r}^{2}+4\ensuremath{\epsilon}r)}{8\ensuremath{\eta}l}$, where $P$ is the driving pressure, $\ensuremath{\epsilon}$ the coefficient of slip and $\ensuremath{\eta}$ the viscosity. By integrating this expression, the distance penetrated by a liquid flowing under capillary pressure alone into a horizontal capillary or one with small internal surface is found to be the square root of ($\frac{\ensuremath{\gamma}\mathrm{rt}\ifmmode\cdot\else\textperiodcentered\fi{}cos\ensuremath{\theta}}{2\ensuremath{\eta}}$), where $\ensuremath{\gamma}$ is the surface tension and $\ensuremath{\theta}$ the angle of contact. The quantity ($\frac{\ensuremath{\gamma}cos\ensuremath{\theta}}{2\ensuremath{\eta}}$) is called the coefficient of penetrance or the penetrativity of the liquid.Penetration of Liquids into a Porous Body.---(1) Theory. If a porous body behaves as an assemblage of very small cylindrical capillaries, the volume which penetrates in a time $t$ would be proportional to the square root of ($\frac{\ensuremath{\gamma}t}{\ensuremath{\eta}}$). (2) Experiments with mercury, water and other liquids completely verify the theoretical deductions.Dynamic capillary method of measuring surface tension is described. It possesses certain advantages on the static method of capillary rise.",
    url = "https://doi.org/10.1103/physrev.17.273",
    doi = "10.1103/physrev.17.273",
    openalex = "W2058046601"
}

@book{goldstein1938modern1,
    author = "Goldstein, S",
    title = "Modern Developments in Fluid Dynamics",
    year = "1938",
    publisher = "Oxford, Oxford University Press",
    note = "talkorigins\_source = {true}; raw\_reference = {Goldstein, S., 1938, Modern Developments in Fluid Dynamics: Oxford, Oxford University Press.}"
}

@article{doi101038144529a0,
    author = "P.P., Lunkenheimer",
    title = "Modern Developments in Fluid Dynamics",
    year = "1939",
    journal = "Nature",
    url = "https://doi.org/10.1038/144529a0",
    doi = "10.1038/144529a0",
    openalex = "W4250635000"
}

@article{doi1023073607555,
    author = "Milne-Thomson, L. M. and Goldstein, S.",
    title = "Modern Developments in Fluid Dynamics",
    year = "1939",
    journal = "The Mathematical Gazette",
    url = "https://doi.org/10.2307/3607555",
    doi = "10.2307/3607555",
    openalex = "W1607439417"
}

@article{doi101243pimeproc194515304902,
    author = "Howell, A.",
    title = "Fluid Dynamics of Axial Compressors",
    year = "1945",
    journal = "Proceedings of the Institution of Mechanical Engineers",
    url = "https://doi.org/10.1243/pime\_proc\_1945\_153\_049\_02",
    doi = "10.1243/pime\_proc\_1945\_153\_049\_02",
    openalex = "W2067344819",
    references = "doi101016s001600321690293x, doi101038144529a0, doi101108eb031311, doi101243pimeproc193914103302, doi102514811313"
}

@article{bleakney1954modern,
    author = "Bleakney, Walker",
    title = "Modern Developments in Fluid Dynamics—High Speed Flow",
    year = "1954",
    journal = "American Journal of Physics",
    url = "https://doi.org/10.1119/1.1933819",
    doi = "10.1119/1.1933819",
    number = "7",
    openalex = "W2048310370",
    pages = "504-504",
    volume = "22"
}

@article{doi10111911933819,
    author = "Bleakney, Walker",
    title = "Modern Developments in Fluid Dynamics—High Speed Flow",
    year = "1954",
    journal = "American Journal of Physics",
    url = "https://doi.org/10.1119/1.1933819",
    doi = "10.1119/1.1933819",
    openalex = "W2048310370"
}

@article{openalexw351281532,
    author = "笠原, 英司",
    title = "〔75〕流体力学の最近の発達(高速流)〔L.Howarth(Editor), Modern Developments in Fluid Dynamics, High Speed Flow, 2 Vols, pp.875, Oxford Univ.Press, 84s.〕",
    year = "1955",
    journal = "日本機械学會誌",
    url = "https://openalex.org/W351281532",
    openalex = "W351281532"
}

Several recent developments in airfoil and wing theory have as thjeir goals the extension of classical methods to account for characteristically viscous phenomena. Airfoil theory has always recognized the existence of such phenomena as explanations of the presence of circulation and vortex wakes; these new investigations are attempts to include detailed descriptions in theoretical models or to extend classical models into areas of strong viscous effects, such as separation and stalling. Some of these studies follow directly from suggestions made by von Karman, and others are reminiscent of his earlier research. This review is concerned with investigations in four categories: (1) the theory of profiles with boundary layers in steady flow, (2) the theory of profiles with boundary layers in unsteady flow, including extensions of unsteady airfoil theory, (3) the theory of wings with leading-edge separation, and (4) Prandtl wing theory applied to partially stalled wings.

@article{doi10251483588,
    author = "Sears, W. R.",
    title = "Some Recent Developments in Airfoil Theory",
    year = "1956",
    journal = "Journal of the aeronautical sciences. [REQUEST TITLE]",
    abstract = "Several recent developments in airfoil and wing theory have as thjeir goals the extension of classical methods to account for characteristically viscous phenomena. Airfoil theory has always recognized the existence of such phenomena as explanations of the presence of circulation and vortex wakes; these new investigations are attempts to include detailed descriptions in theoretical models or to extend classical models into areas of strong viscous effects, such as separation and stalling. Some of these studies follow directly from suggestions made by von Karman, and others are reminiscent of his earlier research. This review is concerned with investigations in four categories: (1) the theory of profiles with boundary layers in steady flow, (2) the theory of profiles with boundary layers in unsteady flow, including extensions of unsteady airfoil theory, (3) the theory of wings with leading-edge separation, and (4) Prandtl wing theory applied to partially stalled wings.",
    url = "https://doi.org/10.2514/8.3588",
    doi = "10.2514/8.3588",
    openalex = "W617440896",
    references = "bleakney1954modern, doi10111911933819"
}

International audience

@misc{openalexw2778033595,
    author = "Годунов, С. К. and Bohachevsky, I.O.",
    title = "Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics",
    year = "1959",
    booktitle = "INRIA a CCSD electronic archive server",
    abstract = "International audience",
    openalex = "W2778033595"
}

Abstract Two‐ and three‐dimensional boundary‐layer equations have been developed for pseudoplastic non‐Newtonian fluids which can be characterized by a power‐law relationship between shear stress and velocity gradient. The types of potential flows necessary for similar solutions to the boundary‐layer equations have been determined. For two‐dimensional flow the results are similar to those obtained for Newtonian fluids. For three‐dimensional flow, however, the possibility of similar solutions depends on the nature of the expression which describes effective viscosity of the fluid. At most, similar solutions are possible only for the case of flow past a flat plate where the potential velocity vector is not perpendicular to the leading edge of the plate; this is a much more restrictive condition than is obtained for Newtonian fluids.

@article{doi101002aic690060105,
    author = "Schowalter, W. R.",
    title = "The application of boundary‐layer theory to power‐law pseudoplastic fluids: Similar solutions",
    year = "1960",
    journal = "AIChE Journal",
    abstract = "Abstract Two‐ and three‐dimensional boundary‐layer equations have been developed for pseudoplastic non‐Newtonian fluids which can be characterized by a power‐law relationship between shear stress and velocity gradient. The types of potential flows necessary for similar solutions to the boundary‐layer equations have been determined. For two‐dimensional flow the results are similar to those obtained for Newtonian fluids. For three‐dimensional flow, however, the possibility of similar solutions depends on the nature of the expression which describes effective viscosity of the fluid. At most, similar solutions are possible only for the case of flow past a flat plate where the potential velocity vector is not perpendicular to the leading edge of the plate; this is a much more restrictive condition than is obtained for Newtonian fluids.",
    url = "https://doi.org/10.1002/aic.690060105",
    doi = "10.1002/aic.690060105",
    openalex = "W2122960191"
}

Abstract A theoretical analysis for the laminar flow past arbitrary external surfaces of non‐Newtonian fluids of the power‐law model is presented. The main problem which is considered is how to predict the drag and the rate of heat transfer from an isothermal surface to the fluid. Inspectional analysis of the modified boundary‐layer equations yields a general relationship both for the drag coefficient and for the Nusselt number as functions of the generalized Reynolds and Prandtl numbers. The flow past a horizontal flat plate is studied in detail numerically.

@article{doi101002aic690060227,
    author = "Acrivos, Andreas and Shah, M. J. and Petersen, Eugene E.",
    title = "Momentum and heat transfer in laminar boundary‐layer flows of non‐Newtonian fluids past external surfaces",
    year = "1960",
    journal = "AIChE Journal",
    abstract = "Abstract A theoretical analysis for the laminar flow past arbitrary external surfaces of non‐Newtonian fluids of the power‐law model is presented. The main problem which is considered is how to predict the drag and the rate of heat transfer from an isothermal surface to the fluid. Inspectional analysis of the modified boundary‐layer equations yields a general relationship both for the drag coefficient and for the Nusselt number as functions of the generalized Reynolds and Prandtl numbers. The flow past a horizontal flat plate is studied in detail numerically.",
    url = "https://doi.org/10.1002/aic.690060227",
    doi = "10.1002/aic.690060227",
    openalex = "W2101943554"
}

A transformation is derived from first principles to reduce the boundary-layer equations for a general compressible two-dimensional flow to incompressible form. For the case of boundary-layer flow of a Newtonian fluid past a smooth wall, but with no other restrictions, it is shown that the combination (ρ∞μ∞/ρwμw) CfReθ is an invariant of the transformation. This result is called the law of corresponding stations. In order to apply the transformation to the problem of the turbulent boundary layer on a smooth wall, it is assumed that the sublayer Reynolds number is unaffected by compressibility or heat transfer provided the density and viscosity are evaluated at a mean sublayer temperature defined by the transformation. Explicit formulas are obtained for the effect of Mach number and heat transfer on surface friction when the fluid is a perfect gas, the pressure is constant, and the stagnation temperature is constant or linear in the velocity. An appendix contains a brief critical discussion of the mean-temperature hypothesis, the laminar-film hypothesis, and other analytical ideas related to the idea of a transformation.

@article{doi10106311711395,
    author = "Coles, Donald",
    title = "The Turbulent Boundary Layer in a Compressible Fluid",
    year = "1964",
    journal = "The Physics of Fluids",
    abstract = "A transformation is derived from first principles to reduce the boundary-layer equations for a general compressible two-dimensional flow to incompressible form. For the case of boundary-layer flow of a Newtonian fluid past a smooth wall, but with no other restrictions, it is shown that the combination (ρ∞μ∞/ρwμw) CfReθ is an invariant of the transformation. This result is called the law of corresponding stations. In order to apply the transformation to the problem of the turbulent boundary layer on a smooth wall, it is assumed that the sublayer Reynolds number is unaffected by compressibility or heat transfer provided the density and viscosity are evaluated at a mean sublayer temperature defined by the transformation. Explicit formulas are obtained for the effect of Mach number and heat transfer on surface friction when the fluid is a perfect gas, the pressure is constant, and the stagnation temperature is constant or linear in the velocity. An appendix contains a brief critical discussion of the mean-temperature hypothesis, the laminar-film hypothesis, and other analytical ideas related to the idea of a transformation.",
    url = "https://doi.org/10.1063/1.1711395",
    doi = "10.1063/1.1711395",
    openalex = "W2096654866"
}

@book{openalexw1484762312,
    author = "Goldstein, Sydney",
    title = "Modern developments in fluid dynamics: an account of theory and experiment relating to boundary layers, turbulent motion and wakes",
    year = "1965",
    url = "https://openalex.org/W1484762312",
    openalex = "W1484762312"
}

Journal Article SIMILARITY SOLUTIONS IN SOME NON-LINEAR DIFFUSION PROBLEMS AND IN BOUNDARY-LAYER FLOW OF A PSEUDO-PLASTIC FLUID Get access C. ATKINSON, C. ATKINSON Department of Mathematics, Imperial CollegeLondon Search for other works by this author on: Oxford Academic Google Scholar C. W. JONES C. W. JONES Department of Mathematics, Imperial CollegeLondon Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Mechanics and Applied Mathematics, Volume 27, Issue 2, May 1974, Pages 193–211, https://doi.org/10.1093/qjmam/27.2.193 Published: 01 May 1974 Article history Received: 26 March 1973 Published: 01 May 1974

@article{doi101093qjmam272193,
    author = "Atkinson, C. and Jones, Chris",
    title = "SIMILARITY SOLUTIONS IN SOME NON-LINEAR DIFFUSION PROBLEMS AND IN BOUNDARY-LAYER FLOW OF A PSEUDO-PLASTIC FLUID",
    year = "1974",
    journal = "The Quarterly Journal of Mechanics and Applied Mathematics",
    abstract = "Journal Article SIMILARITY SOLUTIONS IN SOME NON-LINEAR DIFFUSION PROBLEMS AND IN BOUNDARY-LAYER FLOW OF A PSEUDO-PLASTIC FLUID Get access C. ATKINSON, C. ATKINSON Department of Mathematics, Imperial CollegeLondon Search for other works by this author on: Oxford Academic Google Scholar C. W. JONES C. W. JONES Department of Mathematics, Imperial CollegeLondon Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Mechanics and Applied Mathematics, Volume 27, Issue 2, May 1974, Pages 193–211, https://doi.org/10.1093/qjmam/27.2.193 Published: 01 May 1974 Article history Received: 26 March 1973 Published: 01 May 1974",
    url = "https://doi.org/10.1093/qjmam/27.2.193",
    doi = "10.1093/qjmam/27.2.193",
    openalex = "W2078495712"
}

1 Preliminary Concepts 2 Fundamental Equations of Compressible Viscous Flow 3 Solutions of the Newtonian Viscous-Flow Equations 4 Laminar Boundary Layers 5 The Stability of Laminar Flows 6 Incompressible Turbulent Mean Flow 7 Compressible Boundary Layer Flow Appendices A Transport Properties of Various Newtonian Fluids B Equations of Motion of Incompressible Newtonian Fluids in Cylindrical and Spherical Coordinates C A Runge-Kutta Subroutine for N Simultaneous Differential Equations Bibliography Index

@book{openalexw1523480373,
    author = "White, Frank M.",
    title = "Viscous Fluid Flow",
    year = "1974",
    abstract = "1 Preliminary Concepts 2 Fundamental Equations of Compressible Viscous Flow 3 Solutions of the Newtonian Viscous-Flow Equations 4 Laminar Boundary Layers 5 The Stability of Laminar Flows 6 Incompressible Turbulent Mean Flow 7 Compressible Boundary Layer Flow Appendices A Transport Properties of Various Newtonian Fluids B Equations of Motion of Incompressible Newtonian Fluids in Cylindrical and Spherical Coordinates C A Runge-Kutta Subroutine for N Simultaneous Differential Equations Bibliography Index",
    openalex = "W1523480373"
}

The boundary layer equations for the class of non-Newtonian fluids termed pseudoplastic are examined under the classical conditions of uniform flow past a semi-infinite flat plate. The adoption of Crocco variables results in a nonlinear, singular boundary value problem for the shear function which is an interesting and natural generalization of the well known Crocco equation arising from the standard Newtonian fluid case. The uniqueness, existence and analyticity of the solution are established and subsequently an explicit power series solution is exhibited.

@article{doi1011370138024,
    author = "Nachman, A. and Callegari, Andrew J.",
    title = "A Nonlinear Singular Boundary Value Problem in the Theory of Pseudoplastic Fluids",
    year = "1980",
    journal = "SIAM Journal on Applied Mathematics",
    abstract = "The boundary layer equations for the class of non-Newtonian fluids termed pseudoplastic are examined under the classical conditions of uniform flow past a semi-infinite flat plate. The adoption of Crocco variables results in a nonlinear, singular boundary value problem for the shear function which is an interesting and natural generalization of the well known Crocco equation arising from the standard Newtonian fluid case. The uniqueness, existence and analyticity of the solution are established and subsequently an explicit power series solution is exhibited.",
    url = "https://doi.org/10.1137/0138024",
    doi = "10.1137/0138024",
    openalex = "W2039745296",
    references = "bleakney1954modern, doi101002aic690060105, doi101002aic690060227, doi1010160022247x68902606, doi10106313069011, doi101088003191122611028, doi101093qjmam272193, doi10111911933819, doi1011371017036, doi101215s0012709464031321, doi1023073607555"
}

Applications of second‐moment turbulent closure hypotheses to geophysical fluid problems have developed rapidly since 1973, when genuine predictive skill in coping with the effects of stratification was demonstrated. The purpose here is to synthesize and organize material that has appeared in a number of articles and add new useful material so that a complete (and improved) description of a turbulence model from conception to application is condensed in a single article. It is hoped that this will be a useful reference to users of the model for application to either atmospheric or oceanic boundary layers.

@article{doi101029rg020i004p00851,
    author = "Mellor, George L. and Yamada, Tetsuji",
    title = "Development of a turbulence closure model for geophysical fluid problems",
    year = "1982",
    journal = "Reviews of Geophysics",
    abstract = "Applications of second‐moment turbulent closure hypotheses to geophysical fluid problems have developed rapidly since 1973, when genuine predictive skill in coping with the effects of stratification was demonstrated. The purpose here is to synthesize and organize material that has appeared in a number of articles and add new useful material so that a complete (and improved) description of a turbulence model from conception to application is condensed in a single article. It is hoped that this will be a useful reference to users of the model for application to either atmospheric or oceanic boundary layers.",
    url = "https://doi.org/10.1029/rg020i004p00851",
    doi = "10.1029/rg020i004p00851",
    openalex = "W2038742869",
    references = "doi1010160017931063900358, doi107551mitpress30140010001"
}

@book{doi101007bfb0074528,
    author = "Brezzi, Franco",
    title = "Numerical Methods in Fluid Dynamics",
    year = "1985",
    booktitle = "Lecture notes in mathematics",
    url = "https://doi.org/10.1007/bfb0074528",
    doi = "10.1007/bfb0074528",
    openalex = "W1598812702"
}

Here is an introduction to numerical methods for partial differential equations with particular reference to those that are of importance in fluid dynamics. The author gives a thorough and rigorous treatment of the techniques, beginning with the classical methods and leading to a discussion of modern developments. For easier reading and use, many of the purely technical results and theorems are given separately from the main body of the text. The presentation is intended for graduate students in applied mathematics, engineering and physical sciences who have a basic knowledge of partial differential equations.

@book{doi101017cbo9780511753138,
    author = "Sod, Gary A.",
    title = "Numerical Methods in Fluid Dynamics",
    year = "1985",
    booktitle = "Cambridge University Press eBooks",
    abstract = "Here is an introduction to numerical methods for partial differential equations with particular reference to those that are of importance in fluid dynamics. The author gives a thorough and rigorous treatment of the techniques, beginning with the classical methods and leading to a discussion of modern developments. For easier reading and use, many of the purely technical results and theorems are given separately from the main body of the text. The presentation is intended for graduate students in applied mathematics, engineering and physical sciences who have a basic knowledge of partial differential equations.",
    url = "https://doi.org/10.1017/cbo9780511753138",
    doi = "10.1017/cbo9780511753138",
    openalex = "W4300011631"
}

The wetting of solids by liquids is connected to physical chemistry (wettability), to statistical physics (pinning of the contact line, wetting transitions, etc.), to long-range forces (van der Waals, double layers), and to fluid dynamics. The present review represents an attempt towards a unified picture with special emphasis on certain features of "dry spreading": (a) the final state of a spreading droplet need not be a monomolecular film; (b) the spreading drop is surrounded by a precursor film, where most of the available free energy is spent; and (c) polymer melts may slip on the solid and belong to a separate dynamical class, conceptually related to the spreading of superfluids.

@article{doi101103revmodphys57827,
    author = "de Gennes, P. G.",
    title = "Wetting: statics and dynamics",
    year = "1985",
    journal = "Reviews of Modern Physics",
    abstract = {The wetting of solids by liquids is connected to physical chemistry (wettability), to statistical physics (pinning of the contact line, wetting transitions, etc.), to long-range forces (van der Waals, double layers), and to fluid dynamics. The present review represents an attempt towards a unified picture with special emphasis on certain features of "dry spreading": (a) the final state of a spreading droplet need not be a monomolecular film; (b) the spreading drop is surrounded by a precursor film, where most of the available free energy is spent; and (c) polymer melts may slip on the solid and belong to a separate dynamical class, conceptually related to the spreading of superfluids.},
    url = "https://doi.org/10.1103/revmodphys.57.827",
    doi = "10.1103/revmodphys.57.827",
    openalex = "W2155788949"
}

@book{doi1010079783642841088,
    author = "Canuto, Claudio and Hussaini, M. Yousuff and Quarteroni, Alfio and Zang, Thomas A.",
    title = "Spectral Methods in Fluid Dynamics",
    year = "1988",
    url = "https://doi.org/10.1007/978-3-642-84108-8",
    doi = "10.1007/978-3-642-84108-8",
    openalex = "W4298060601"
}

In this paper we describe a new approximate Riemann solver for compressible gas flow. In contrast to previous Riemann solvers, where a numerical approximation for the pressure and the velocity at the contact discontinuity is computed, we derive a numerical approximation for the largest and smallest signal velocity in the Riemann problem. Having obtained the numerical signal velocities, we use theoretical results by Harten, Lax and van Leer to obtain the full approximation. A stability condition for the numerical signal velocities is derived. We also demonstrate a relation between the signal velocities and the dissipation contained in the corresponding Godunov-type method. The computation of signal velocities for a general (convex) equation of state is discussed. Numerical results for the one- and two-dimensional compressible gas dynamics equations are also given.

@article{doi1011370725021,
    author = "Einfeldt, Bernd",
    title = "On Godunov-Type Methods for Gas Dynamics",
    year = "1988",
    journal = "SIAM Journal on Numerical Analysis",
    abstract = "In this paper we describe a new approximate Riemann solver for compressible gas flow. In contrast to previous Riemann solvers, where a numerical approximation for the pressure and the velocity at the contact discontinuity is computed, we derive a numerical approximation for the largest and smallest signal velocity in the Riemann problem. Having obtained the numerical signal velocities, we use theoretical results by Harten, Lax and van Leer to obtain the full approximation. A stability condition for the numerical signal velocities is derived. We also demonstrate a relation between the signal velocities and the dissipation contained in the corresponding Godunov-type method. The computation of signal velocities for a general (convex) equation of state is discussed. Numerical results for the one- and two-dimensional compressible gas dynamics equations are also given.",
    url = "https://doi.org/10.1137/0725021",
    doi = "10.1137/0725021",
    openalex = "W2171431553",
    references = "doi101006jcph19975705, doi1010079781468401523, doi101016002199917790095x, doi1010160021999178900232, doi1010160021999179901451, doi1010160021999181901285, doi1010160021999183901365, doi1010160021999184901426, doi1010160021999184901438, doi101017cbo9780511753138, doi1011371025002"
}

Liquid crystals are remarkably useful for laboratory exploration of the dynamics of cosmologically relevant defects. They are convenient to work with, they allow the direct study of the "scaling solution" for a network of strings, and they provide a model for the evolution of monopoles and texture. Experiments described here support the simple "one-scale" model for cosmic string evolution, as well as some qualitative predictions of string statistical mechanics. The structure of monopoles and their apparent cylindrical but not spherical symmetry is discussed. A particular kind of defect known as texture is described and is shown to have a dynamical instability-it can decay into a monopole-antimonopole pair. This decay process has been observed occurring in the liquid crystal, and studied with numerical simulations.

@article{doi101126science25149991336,
    author = "Chuang, Isaac L. and Durrer, Ruth and Turok, Neil and Yurke, Bernard",
    title = "Cosmology in the Laboratory: Defect Dynamics in Liquid Crystals",
    year = "1991",
    journal = "Science",
    abstract = {Liquid crystals are remarkably useful for laboratory exploration of the dynamics of cosmologically relevant defects. They are convenient to work with, they allow the direct study of the "scaling solution" for a network of strings, and they provide a model for the evolution of monopoles and texture. Experiments described here support the simple "one-scale" model for cosmic string evolution, as well as some qualitative predictions of string statistical mechanics. The structure of monopoles and their apparent cylindrical but not spherical symmetry is discussed. A particular kind of defect known as texture is described and is shown to have a dynamical instability-it can decay into a monopole-antimonopole pair. This decay process has been observed occurring in the liquid crystal, and studied with numerical simulations.},
    url = "https://doi.org/10.1126/science.251.4999.1336",
    doi = "10.1126/science.251.4999.1336",
    openalex = "W1984060692",
    references = "doi101103physrevlett64119"
}

A liquid being ejected from a nozzle emanates from it as discrete, uniformly sized drops when the flow rate is sufficiently low. In this paper, an experimental study is presented of the dynamics of a viscous liquid drop that is being formed directly at the tip of a vertical tube into ambient air. The evolution in time of the drop shape and volume is monitored with a time resolution of 1/12 to 1 ms. Following the detachment of the previous drop, the profile of the new growing drop at first changes from spherical to pear-shaped. As time advances, the throat of the pear-shaped drop takes on the appearance of a liquid thread that connects the bottom portion of the drop that is about to detach to the rest of the liquid that is pendant from the tube. The focus here is on probing the effects of physical and geometric parameters on the universal features of drop formation, paying special attention to the development, extension, and breakup of the liquid thread and the satellite drops that are formed subsequent to its breakup. The role of surfactants in modifying the dynamics of drop formation is also studied. The effects of finite inertial, capillary, viscous, and gravitational forces are all accounted for to classify drastically different formation dynamics and to elucidate the fate of satellite drops following thread rupture.

@article{doi1010631868577,
    author = "Zhang, Xiaoguang and Basaran, Osman A.",
    title = "An experimental study of dynamics of drop formation",
    year = "1995",
    journal = "Physics of Fluids",
    abstract = "A liquid being ejected from a nozzle emanates from it as discrete, uniformly sized drops when the flow rate is sufficiently low. In this paper, an experimental study is presented of the dynamics of a viscous liquid drop that is being formed directly at the tip of a vertical tube into ambient air. The evolution in time of the drop shape and volume is monitored with a time resolution of 1/12 to 1 ms. Following the detachment of the previous drop, the profile of the new growing drop at first changes from spherical to pear-shaped. As time advances, the throat of the pear-shaped drop takes on the appearance of a liquid thread that connects the bottom portion of the drop that is about to detach to the rest of the liquid that is pendant from the tube. The focus here is on probing the effects of physical and geometric parameters on the universal features of drop formation, paying special attention to the development, extension, and breakup of the liquid thread and the satellite drops that are formed subsequent to its breakup. The role of surfactants in modifying the dynamics of drop formation is also studied. The effects of finite inertial, capillary, viscous, and gravitational forces are all accounted for to classify drastically different formation dynamics and to elucidate the fate of satellite drops following thread rupture.",
    url = "https://doi.org/10.1063/1.868577",
    doi = "10.1063/1.868577",
    openalex = "W2066895053",
    references = "doi101016s0065237708601866"
}

We present a detailed numerical study of the interaction of a weak shock wave with an isolated cylindrical gas inhomogeneity. Such interactions have been studied experimentally in an attempt to elucidate the mechanisms whereby shock waves propagating through random media enhance mixing. Our study concentrates on the early phases of the interaction process which are dominated by repeated refractions and reflections of acoustic fronts at the bubble interface. Specifically, we have reproduced two of the experiments performed by Haas & Sturtevant: a Mach 1.22 planar shock wave, moving through air, impinges on a cylindrical bubble which contains either helium or Refrigerant 22. These flows are modelled using the two-dimensional compressible Euler equations for a two-component fluid (air-helium or air–Refrigerant 22). Utilizing a novel shock-capturing scheme in conjunction with a sophisticated mesh refinement algorithm, we have been able to reproduce numerically the intricate mechanisms that were observed experimentally, e.g. transition from regular to irregular refraction, cusp formation and shock wave focusing, multi-shock and Mach shock structures, and jet formation. The level of agreement lends credibility to a number of observations that can be made using information from the simulations for which there is no experimental counterpart. Thus we can now present an updated description for the dynamics of a shock-bubble interaction which goes beyond that provided by the original experiments.

@article{doi101017s0022112096007069,
    author = "Quirk, James J. and Karni, Smadar",
    title = "On the dynamics of a shock–bubble interaction",
    year = "1996",
    journal = "Journal of Fluid Mechanics",
    abstract = "We present a detailed numerical study of the interaction of a weak shock wave with an isolated cylindrical gas inhomogeneity. Such interactions have been studied experimentally in an attempt to elucidate the mechanisms whereby shock waves propagating through random media enhance mixing. Our study concentrates on the early phases of the interaction process which are dominated by repeated refractions and reflections of acoustic fronts at the bubble interface. Specifically, we have reproduced two of the experiments performed by Haas \& Sturtevant: a Mach 1.22 planar shock wave, moving through air, impinges on a cylindrical bubble which contains either helium or Refrigerant 22. These flows are modelled using the two-dimensional compressible Euler equations for a two-component fluid (air-helium or air–Refrigerant 22). Utilizing a novel shock-capturing scheme in conjunction with a sophisticated mesh refinement algorithm, we have been able to reproduce numerically the intricate mechanisms that were observed experimentally, e.g. transition from regular to irregular refraction, cusp formation and shock wave focusing, multi-shock and Mach shock structures, and jet formation. The level of agreement lends credibility to a number of observations that can be made using information from the simulations for which there is no experimental counterpart. Thus we can now present an updated description for the dynamics of a shock-bubble interaction which goes beyond that provided by the original experiments.",
    url = "https://doi.org/10.1017/s0022112096007069",
    doi = "10.1017/s0022112096007069",
    openalex = "W2123280614",
    references = "doi101017s0022112058000495"
}

The loose coupling of computational fluid dynamics and computational structural dynamics solvers introduces some problems related to the information transfer between the codes. Some techniques developed to solve the problems of the load transfer and interface surface tracking are presented. The main criterion is to achieve conservation of total loads and total energy. The load projection scheme is based on Gaussian integration and fast interpolation algorithms for unstructured grids. The surface tracking algorithm, also based on interpolation, is important for many applications, including aeroelastic deformation of wings due to aerodynamic loads. The methodologies not only improve present fluid-structure interaction simulations, but also increase the range of their applicability. These techniques are of general character and can be used in other multidisciplinary applications as well.

@article{doi1025142158,
    author = "Cebral, Juan R. and Löhner, Rainald",
    title = "Conservative Load Projection and Tracking for Fluid-Structure Problems",
    year = "1997",
    journal = "AIAA Journal",
    abstract = "The loose coupling of computational fluid dynamics and computational structural dynamics solvers introduces some problems related to the information transfer between the codes. Some techniques developed to solve the problems of the load transfer and interface surface tracking are presented. The main criterion is to achieve conservation of total loads and total energy. The load projection scheme is based on Gaussian integration and fast interpolation algorithms for unstructured grids. The surface tracking algorithm, also based on interpolation, is important for many applications, including aeroelastic deformation of wings due to aerodynamic loads. The methodologies not only improve present fluid-structure interaction simulations, but also increase the range of their applicability. These techniques are of general character and can be used in other multidisciplinary applications as well.",
    url = "https://doi.org/10.2514/2.158",
    doi = "10.2514/2.158",
    openalex = "W1989234930",
    references = "doi101002fld1650071007"
}

@incollection{doi10100797836620388265,
    author = "Shu, Chi‐Wang",
    title = "High Order ENO and WENO Schemes for Computational Fluid Dynamics",
    year = "1999",
    booktitle = "Lecture notes in computational science and engineering",
    url = "https://doi.org/10.1007/978-3-662-03882-6\_5",
    doi = "10.1007/978-3-662-03882-6\_5",
    openalex = "W157107253",
    references = "doi101006jcph19941155, doi101006jcph19960130, doi101006jcph19975705, doi1010079783034886291, doi1010160021999179901451, doi1010160021999181901285, doi1010160021999183901365, doi1010160021999188900022, doi1010160021999188901775, doi1010160021999189902222, doi101017cbo9780511753138"
}

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

@article{doi10251427048,
    author = "Driest, E. R. Van",
    title = "Turbulent Boundary Layer in Compressible Fluids",
    year = "2003",
    journal = "Journal of Spacecraft and Rockets",
    abstract = "Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.",
    url = "https://doi.org/10.2514/2.7048",
    doi = "10.2514/2.7048",
    openalex = "W2095023166"
}

Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the P\'eclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world.

@article{doi101103revmodphys77977,
    author = "Squires, Todd M. and Quake, Stephen R.",
    title = "Microfluidics: Fluid physics at the nanoliter scale",
    year = "2005",
    journal = "Reviews of Modern Physics",
    abstract = "Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the P\'eclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world.",
    url = "https://doi.org/10.1103/revmodphys.77.977",
    doi = "10.1103/revmodphys.77.977",
    openalex = "W2020438216",
    references = "doi1010021522268320001221183931aidelps393130co2m, doi1010079789400983526, doi101021ja01639a090, doi101038144529a0, doi10106313058072, doi101098rspa19530139, doi101103physrev17273, doi101103revmodphys57827, doi101119110903, doi101146annurevmatsci281153, doi101201b17118, doi1023073607555, doi105860choice332140, openalexw2065318865"
}

In the early development of gas turbines, many empirical design rules were used; for example in obtaining fluid deflection using the deviation from blading angles, in the assumption of zero radial velocities (so-called radial equilibrium) and in expressions for clearance loss (the Lakshminarayana formulas). The validity of some of these rules, and the basic fluid mechanics behind them, is examined by use of modern ideas and computational fluid dynamics (CFD) codes. A current perspective of CFD in design is given, together with a view on future developments.

@article{doi10111511650379,
    author = "Horlock, J. H. and Denton, J. D.",
    title = "A Review of Some Early Design Practice Using Computational Fluid Dynamics and a Current Perspective",
    year = "2005",
    journal = "Journal of Turbomachinery",
    abstract = "In the early development of gas turbines, many empirical design rules were used; for example in obtaining fluid deflection using the deviation from blading angles, in the assumption of zero radial velocities (so-called radial equilibrium) and in expressions for clearance loss (the Lakshminarayana formulas). The validity of some of these rules, and the basic fluid mechanics behind them, is examined by use of modern ideas and computational fluid dynamics (CFD) codes. A current perspective of CFD in design is given, together with a view on future developments.",
    url = "https://doi.org/10.1115/1.1650379",
    doi = "10.1115/1.1650379",
    openalex = "W2029538994",
    references = "doi101243pimeproc194515304902"
}

The role of the swash zone in influencing the whole nearshore dynamics is reviewed with a focus on the interaction between surf and swash zone processes. Local and global hydromorphodynamic phenomena are discussed in detail, and a description of the overall swash zone operation is given. The effects of swash zone boundary conditions are highlighted, together with the importance of surf zone boundary conditions. Major emphasis is placed on illustrating the interactions of various hydrodynamic modes which, in turn, control the swash and surf zone morphology. Finally, methods to account for swash zone processes in coastal models with different temporal and spatial resolutions are proposed.

@article{doi1010292006rg000215,
    author = "Brocchini, Maurizio and Baldock, Tom E.",
    title = "Recent advances in modeling swash zone dynamics: Influence of surf‐swash interaction on nearshore hydrodynamics and morphodynamics",
    year = "2008",
    journal = "Reviews of Geophysics",
    abstract = "The role of the swash zone in influencing the whole nearshore dynamics is reviewed with a focus on the interaction between surf and swash zone processes. Local and global hydromorphodynamic phenomena are discussed in detail, and a description of the overall swash zone operation is given. The effects of swash zone boundary conditions are highlighted, together with the importance of surf zone boundary conditions. Major emphasis is placed on illustrating the interactions of various hydrodynamic modes which, in turn, control the swash and surf zone morphology. Finally, methods to account for swash zone processes in coastal models with different temporal and spatial resolutions are proposed.",
    url = "https://doi.org/10.1029/2006rg000215",
    doi = "10.1029/2006rg000215",
    openalex = "W1997962158",
    references = "doi101017s0022112058000495"
}

A simple but effective technique is proposed to generate cylindrical converging shock waves. The shock dynamics is employed to design a curved wall profile of the test section in a shock tube. When a planar shock wave propagates forward along the curved wall, the disturbances produced by the curved wall would continuously propagate along the shock surface and bend the shock wave. As an example, the wall profile for an incident shock Mach number of M0=1.2 and a converging angle of 15° is tested numerically and experimentally. Both numerical and experimental results show a perfect circular shock front, which validates our method.

@article{doi10106313392603,
    author = "Zhai, Zhigang and Liu, Cangli and Qin, Fenghua and Yang, Jiming and Luo, Xisheng",
    title = "Generation of cylindrical converging shock waves based on shock dynamics theory",
    year = "2010",
    journal = "Physics of Fluids",
    abstract = "A simple but effective technique is proposed to generate cylindrical converging shock waves. The shock dynamics is employed to design a curved wall profile of the test section in a shock tube. When a planar shock wave propagates forward along the curved wall, the disturbances produced by the curved wall would continuously propagate along the shock surface and bend the shock wave. As an example, the wall profile for an incident shock Mach number of M0=1.2 and a converging angle of 15° is tested numerically and experimentally. Both numerical and experimental results show a perfect circular shock front, which validates our method.",
    url = "https://doi.org/10.1063/1.3392603",
    doi = "10.1063/1.3392603",
    openalex = "W2047375898",
    references = "doi101017s0022112058000495"
}

@article{doi101016jenconman201507042,
    author = "Su, Mingze and Zhao, Haibo and Ma, Jinchen",
    title = "Computational fluid dynamics simulation for chemical looping combustion of coal in a dual circulation fluidized bed",
    year = "2015",
    journal = "Energy Conversion and Management",
    url = "https://doi.org/10.1016/j.enconman.2015.07.042",
    doi = "10.1016/j.enconman.2015.07.042",
    openalex = "W2220918762",
    references = "doi1010160307904x86900454"
}