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Engquist, Bjorn; Osher, Stanley

One-sided difference approximations for nonlinear conservation laws. (English) Zbl 0469.65067

Math. Comput. 36, 321-351 (1981).
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Cited in 4 Reviews
Cited in 90 Documents

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
76L05 Shock waves and blast waves in fluid mechanics

Keywords:

upwind finite difference approximations; nonlinear conservation laws; nonlinear stability; entropy condition; shock calculations; numerical examples
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\textit{B. Engquist} and \textit{S. Osher}, Math. Comput. 36, 321--351 (1981; Zbl 0469.65067)
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References:

[1] Michael G. Crandall and Andrew Majda, Monotone difference approximations for scalar conservation laws, Math. Comp. 34 (1980), no. 149, 1 – 21. · Zbl 0423.65052
[2] Germund G. Dahlquist, A special stability problem for linear multistep methods, Nordisk Tidskr. Informations-Behandling 3 (1963), 27 – 43. · Zbl 0123.11703
[3] Germund Dahlquist, Positive functions and some applications to stability questions for numerical methods, Recent advances in numerical analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1978) Publ. Math. Res. Center Univ. Wisconsin, vol. 41, Academic Press, New York-London, 1978, pp. 1 – 29. · Zbl 0457.65049
[4] Björn Engquist and Stanley Osher, Stable and entropy satisfying approximations for transonic flow calculations, Math. Comp. 34 (1980), no. 149, 45 – 75. · Zbl 0438.76051
[5] Amiram Harten, The artificial compression method for computation of shocks and contact discontinuities. I. Single conservation laws, Comm. Pure Appl. Math. 30 (1977), no. 5, 611 – 638. · Zbl 0343.76023
[6] 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. · Zbl 0351.76070
[7] Antony Jameson, Numerical solution of nonlinear partial differential equations of mixed type, Numerical solution of partial differential equations, III (Proc. Third Sympos. (SYNSPADE), Univ. Maryland, College Park, Md., 1975) Academic Press, New York, 1976, pp. 275 – 320.
[8] Gray Jennings, Discrete shocks, Comm. Pure Appl. Math. 27 (1974), 25 – 37. · Zbl 0304.65063
[9] J. A. Krupp & J. D. Cole, Studies in Transonic Flow IV, Unsteady Transonic Flow, UCLA Eng. Dept. Rep., 76/04, 1976.
[10] Peter Lax, Shock waves and entropy, Contributions to nonlinear functional analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971) Academic Press, New York, 1971, pp. 603 – 634. · Zbl 0268.35014
[11] Peter Lax and Burton Wendroff, Systems of conservation laws, Comm. Pure Appl. Math. 13 (1960), 217 – 237. · Zbl 0152.44802
[12] E. M. Murman & J. D. Cole, ”Calculations of steady transonic flows,” AIAA J., v. 9, 1971, pp. 114-121. · Zbl 0249.76033
[13] Patrick J. Roache, Computational fluid dynamics, Hermosa Publishers, Albuquerque, N.M., 1976. With an appendix (”On artificial viscosity”) reprinted from J. Computational Phys. 10 (1972), no. 2, 169 – 184; Revised printing. · Zbl 0247.76035
[14] Joseph L. Steger, Coefficient matrices for implicit finite difference solution of the inviscid fluid conservation law equations, Comput. Methods Appl. Mech. Engrg. 13 (1978), no. 2, 175 – 188. · Zbl 0382.76061
[15] Gilbert Strang, Accurate partial difference methods. II. Non-linear problems, Numer. Math. 6 (1964), 37 – 46. · Zbl 0143.38204
[16] B. van Leer, ”Towards the ultimate conservative difference scheme III-Upstream-centered finite-difference schemes for ideal compressible flow,” J. Comput. Phys., v. 3, 1977, pp. 263-275. · Zbl 0339.76039
[17] B. van Leer, ”Towards the ultimate conservative difference scheme IV; A new approach to numerical convection,” J. Comput. Phys., v. 23, 1977, pp. 276-299. · Zbl 0339.76056
[18] 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. · Zbl 0364.76047
[19] R. F. Warming and Richard M. Beam, On the construction and application of implicit factored schemes for conservation laws, Computational fluid dynamics (Proc. SIAM-AMS Sympos. Appl. Math., New York, 1977) Amer. Math. Soc., Providence, R.I., 1978, pp. 85 – 129. SIAM-AMS Proc., Vol. XI. · Zbl 0392.65038
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