Three-dimensional second-order accurate difference schemes for discontinuous hydrodynamic flows

Authors:
Ephraim L. Rubin and Stanley Preiser

Journal:
Math. Comp. **24** (1970), 57-63

MSC:
Primary 76.65

DOI:
https://doi.org/10.1090/S0025-5718-1970-0264904-4

MathSciNet review:
0264904

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we show how a second-order accurate two-step method used in the numerical computation of hydrodynamic flows may be derived directly from the integral conservation laws. A necessary and sufficient condition for stability for the linearized equations is derived for the three-dimensional Cartesian coordinate case.

**[1]**J. L. Anderson, S. Preiser & E. L. Rubin, "Conservation form of the equations of hydrodynamics in curvilinear coordinate systems,"*J. Computational Phys.*, v. 2, 1968, pp. 279-287.**[2]**P. D. Lax & B. Wendroff, "Systems of conservation laws,"*Comm. Pure Appl. Math.*, v. 13, 1960, pp. 217-237. MR**22**#11523. MR**0120774 (22:11523)****[3]**R. D. Richtmyer,*A Survey of Difference Methods for Non-Steady Fluid Dynamics*, NCAR Technical Note 63-2, 1962.**[4]**E. L. Rubin & S. Z. Burstein, "Difference methods for the inviscid and viscous equations of a compressible gas,"*J. Computational Phys.*, v. 2, 1967, pp. 178-196.**[5]**C. Truesdell & R. Toupin,*The Classical Field Theories*, Handbuch der Physik, Band III/I, Springer-Verlag, Berlin, 1960. MR**22**#8778. MR**0118005 (22:8778)****[6]**A. H. Taub,*On the Derivation of Difference Equations for Hydrodynamics*, Los Alamos Scientific Laboratory Report LA-2073, 1957.**[7]**L. P. Eisenhart,*Continuous Groups of Transformations*, Dover, New York, 1961, p. 208. MR**23**#A1328. MR**0124008 (23:A1328)****[8]**H.-O. Kreiss, "On difference approximations of the dissipative type for hyperbolic differential equations,"*Comm. Pure Appl. Math.*, v. 17, 1964, pp. 335-353. MR**29**#4210. MR**0166937 (29:4210)**

Retrieve articles in *Mathematics of Computation*
with MSC:
76.65

Retrieve articles in all journals with MSC: 76.65

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0264904-4

Keywords:
Fluid dynamics,
stability,
conservation laws

Article copyright:
© Copyright 1970
American Mathematical Society