Computation of steady shocks by second-order finite-difference schemes

Author:
Lasse K. Karlsen

Journal:
Math. Comp. **34** (1980), 391-400

MSC:
Primary 65M10; Secondary 76L05

DOI:
https://doi.org/10.1090/S0025-5718-1980-0559192-1

MathSciNet review:
559192

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Abstract: The computational stability of steady shocks which satisfy the entropy condition is considered for the scalar conservation law

**[1]**A. HARTEN, J. M. HYMAN & P. D. LAX, ``On finite-difference approximations and entropy conditions for shocks,''*Comm. Pure Appl. Math.*, v. 29, 1976, pp. 297-322. MR**0413526 (54:1640)****[2]**O. A. OLEINIK, ``Discontinuous solutions of nonlinear differential equations,''*Uspehi Mat. Nauk,*v. 12, 1957, pp. 3-73; English transl.,*Amer. Math. Soc. Transl.*(2), v. 26, 1963, pp. 95-172. MR**0151737 (27:1721)****[3]**H.-O. KREISS, ``Difference approximations for initial-boundary value problems for hyperbolic differential equations,'' in*Numerical Solutions of Nonlinear Partial Differential Equations*(D. Greenspan, Ed.), Wiley, New York, 1966, pp. 114-166. MR**0214305 (35:5156)****[4]**R. D. RICHTMEYER & K. W. MORTON,*Difference Methods for Initial Value Problems*, Interscience, New York, 1967.**[5]**R. W. MacCORMACK,*The Effect of Viscosity in Hypervelocity Impact Cratering*, AIAA Paper 69-354, 1969.**[6]**L. K. KARLSEN,*A Criterion for the Existence of Erroneous Modes Near Steady Shocks in Conservative Finite-Difference Computations*, Trans. Roy. Inst. Techn., TRITA-FPT-009, Stockholm, 1974.**[7]**R. F. WARMING & R. M. BEAM, ``Upwind second-order difference schemes and applications in unsteady aerodynamic flows,''*AIAA J.*, v. 14, 1976, pp. 1241-1249. MR**0459301 (56:17495)**

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DOI:
https://doi.org/10.1090/S0025-5718-1980-0559192-1

Article copyright:
© Copyright 1980
American Mathematical Society