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, and P. D. Lax,*On finite-difference approximations and entropy conditions for shocks*, Comm. Pure Appl. Math.**29**(1976), no. 3, 297–322. With an appendix by B. Keyfitz. MR**0413526**, https://doi.org/10.1002/cpa.3160290305**[2]**O. A. Oleĭnik,*Discontinuous solutions of non-linear differential equations*, Amer. Math. Soc. Transl. (2)**26**(1963), 95–172. MR**0151737****[3]**Heinz-Otto Kreiss,*Difference approximations for the initial-boundary value problem for hyperbolic differential equations*, Numerical Solutions of Nonlinear Differential Equations (Proc. Adv. Sympos., Madison, Wis., 1966) John Wiley & Sons, Inc., New York, 1966, pp. 141–166. MR**0214305****[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 and Richard M. Beam,*Upwind second-order difference schemes and applications in aerodynamic flows*, AIAA J.**14**(1976), no. 9, 1241–1249. MR**0459301**, https://doi.org/10.2514/3.61457

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

Article copyright:
© Copyright 1980
American Mathematical Society