The Numerical Approach to Hydrodynamic Problems

Interest in the numerical solution of hydrodynamic problems has been alive for a long time; the book of ref. 1, for instance, bears the date 1922. The reasons of the interest are obvious: so few explicit solutions of the equations of hydrodynamics are known and great gaps still exist in the knowledge on the qualitative behaviour of general solutions [2, 3]. As ref. 1 already shows, attempts at numerical integration were made before the age of computers: some references to this earlier work can be found in the textbooks of Allen [4] and Thorn–Ape It [5], among others.

[1]  B. J. Daly.  Numerical Study of Two Fluid Rayleigh‐Taylor Instability , 1967 .

[2]  W. Velte.  Stabilität und Verzweigung stationärer Lösungen der Navier-Stokesschen Gleichungen beim Taylorproblem , 1966 .

[3]  F. Harlow,et al.  THE MAC METHOD-A COMPUTING TECHNIQUE FOR SOLVING VISCOUS, INCOMPRESSIBLE, TRANSIENT FLUID-FLOW PROBLEMS INVOLVING FREE SURFACES , 1965 .

[4]  D. Allen,et al.  Relaxation methods in engineering and science , 1954 .

[5]  L. H. Thomas.  THE STABILITY OF PLANE POISEUILLE FLOW , 1952 .

[6]  G. Ghelardoni.  Considerazioni numeriche su un problema di idrodinamica , 1967 .

[7]  Ratip Berker.  Sur quelques cas d'integration des équations du mouvement d'un fluide visqueux incompressible , 1936 .

[8]  NUMERICAL STUDIES OF THE NAVIER-STOKES EQUATIONS. , 1964 .

[9]  L. C. Woods,et al.  Field Computations in Engineering and Physics , 1962 .

[10]  M. Abbott.  A NUMERICAL METHOD FOR SOLVING THE EQUATIONS OF NATURAL CONVECTION IN A NARROW CONCENTRIC CYLINDRICAL ANNULUS WITH A HORIZONTAL AXIS , 1963 .

[11]  Jacob E. Fromm,et al.  Numerical Solution of the Problem of Vortex Street Development , 1963 .

[12]  F. Harlow,et al.  Liquid Waves by Computer , 1965, Science.

[13]  G. Taylor.  Stability of a Viscous Liquid Contained between Two Rotating Cylinders , 1923 .

[14]  Lewis F. Richardson,et al.  Weather Prediction by Numerical Process , 1922 .

[15]  R. Donnelly,et al.  EXPERIMENTS ON THE STABILITY OF SPIRAL FLOW BETWEEN ROTATING CYLINDERS. , 1960, Proceedings of the National Academy of Sciences of the United States of America.

[16]  K. Kirchgässner.  Die Instabilität der Strömung zwischen zwei rotierenden Zylindern gegenüber Taylor-Wirbeln für beliebige Spaltbreiten , 1961 .

[17]  H. Witting.  Über den einfluβ der stromlinienkrümmung auf die stabilität laminarer strömungen , 1958 .

[18]  J. Gillis,et al.  Methods in Computational Physics , 1964 .

[19]  S. Chandrasekhar.  Hydrodynamic and Hydromagnetic Stability , 1961 .

[20]  A. H. Taub,et al.  A study of a numerical solution to a two-dimensional hydrodynamical problem , 1959 .

[21]  Ettore Bellomo.  A numerical program for dealing with finite-amptlitude disturbances in plane parallel laminar flows , 1967 .

[22]  S. Ulam,et al.  Heuristic Numerical Work in Some Problems of Hydrodynamics , 1959 .

[23]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[24]  F. Harlow,et al.  Dynamics and Heat Transfer in the von Kármán Wake of a Rectangular Cylinder , 1964 .

[25]  John A. T. Bye,et al.  Obtaining Solutions of the Navier-Stokes Equation by Relaxation Processes , 1965, Comput. J..

[26]  W. Velte.  Stabilitätsverhalten und verzweigung stationärer Lösungen der navier-stokesschen gleichungen , 1964 .

[27]  Francis H. Harlow,et al.  Numerical Study of Large‐Amplitude Free‐Surface Motions , 1966 .

[28]  Jacob E. Fromm,et al.  Computer Experiments in Fluid Dynamics , 1965 .

[29]  G. Lombardi,et al.  Numerical Study of the Stability Problem for Couette Flow , 1966 .

[30]  G. Ghelardoni.  Questioni connesse coll’impostazione analitica e la soluzione numerica di un problema di idrodinamica , 1966 .

[31]  Studio numerico della stabilità del moto di un fluido viscoso in un canale , 1966 .