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Symmetrization of the fluid dynamic matrices with applications


Author: Eli Turkel
Journal: Math. Comp. 27 (1973), 729-736
MSC: Primary 65M10
DOI: https://doi.org/10.1090/S0025-5718-1973-0329279-3
MathSciNet review: 0329279
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Abstract: The matrices occurring in the equations of inviscid fluid dynamics are simultaneously symmetrized by a similarity transformation. The resulting matrices decompose into several lower-dimensional blocks. In addition these blocks are more sparse than previously obtained. These properties are then used to find a sufficiency proof for an improved version of the two-step Richtmyer method.


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  • [1] S. Z. Burstein, "Finite difference calculations for hydrodynamic flows containing discontinuities," J. Computational Phys., v. 1, 1966, pp. 198-222.
  • [2] B. Eilon, D. Gottlieb & G. Zwas, "Numerical stabilizers and computing time for second order accurate schemes," J. Computational Phys., v. 9, 1972, pp. 387-397. MR 0300471 (45:9517)
  • [3] K. O. Friedrichs & P. D. Lax, "Systems of conservation equations with a convex extension," Proc. Nat. Acad. Sci. U.S.A., v. 68, 1971, pp. 1686-1688. MR 44 #3016. MR 0285799 (44:3016)
  • [4] S. K. Godunov, "The problem of a generalized solution in the theory of quasi-linear equations and in gas dynamics," Uspehi Mat. Nauk, v. 17, 1962, no. 3 (105), pp. 147-158 = Russian Math. Surveys, v. 17, 1962, no. 3, pp. 145-156. MR 27 #5445. MR 0155511 (27:5445)
  • [5] A. Kasahara & D. Houghton, "An example of nonunique discontinuous solutions in fluid dynamics," J. Computational Phys., v. 4, 1969, pp. 377-388.
  • [6] 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)
  • [7] P. D. Lax & B. Wendroff, "Difference schemes for hyperbolic equations with higher order accuracy," Comm. Pure Appl. Math., v. 17, 1964, pp. 381-398. MR 30 #722. MR 0170484 (30:722)
  • [8] R. D. Richtmyer & K. W. Morton, Difference Methods for Initial Value Problems, 2nd ed., Interscience, New York, 1967. MR 36 #3515. MR 0220455 (36:3515)
  • [9] G. W. Strang, "Accurate partial difference methods. II: Nonlinear problems," Numer. Math., v. 6, 1964, pp. 37-46. MR 29 #4215. MR 0166942 (29:4215)
  • [10] G. W. Strang, "On the construction and comparison of difference schemes, "SIAM J. Numer. Anal., v. 5, 1968, pp. 506-517. MR 38 #4057. MR 0235754 (38:4057)
  • [11] G. Zwas, "On two step Lax-Wendroff methods in several dimensions," Numer. Math. (To appear.) MR 0323126 (48:1484)

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DOI: https://doi.org/10.1090/S0025-5718-1973-0329279-3
Article copyright: © Copyright 1973 American Mathematical Society

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