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Stable and entropy satisfying approximations for transonic flow calculations

Authors: Björn Engquist and Stanley Osher
Journal: Math. Comp. 34 (1980), 45-75
MSC: Primary 65M10; Secondary 65M05, 76H05
Corrigendum: Math. Comp. 34 (1980), 652.
MathSciNet review: 551290
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Abstract: Finite difference approximations for the small disturbance equation of transonic flow are developed and analyzed. New schemes of the Cole-Murman type are presented for which nonlinear stability is proved. The Cole-Murman scheme may have entropy violating expansion shocks as solutions. In the new schemes the switch between the subsonic and supersonic domains is designed such that these nonphysical shocks are guaranteed not to occur. Results from numerical calculations are given which illustrate these conclusions.

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  • [1] W. F. BALLHAUS & P. M. GOORJIAN, Implicit Finite Difference Computation of Unsteady Transonic Flow About Airfoils Including the Treatment of Irregular Shock Wave Motions, A.I.A.A. paper No. 77-205, 1977.
  • [2] J. D. COLE, "Modern developments in transonic flow," SIAM J. Appl. Math., v. 29, 1975, pp. 763-786. MR 0386435 (52:7289)
  • [3] M. G. CRANDALL & A. MAJDA, "Monotone difference approximations for scalar conservation laws." (To appear.) MR 551288 (81b:65079)
  • [4] B. ENGQUIST & A. MAJDA, "Numerical radiation boundary conditions for unsteady transonic flow," J. Computational Phys. (Submitted.)
  • [5] 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)
  • [6] A. JAMESON, "Numerical solutions of nonlinear partial differential equations of mixed type," Numerical Solutions of Partial Differential Equations III, Academic Press, New York, 1976, pp. 275-320. MR 0468255 (57:8093)
  • [7] G. JENNINGS, "Discrete shocks," Comm. Pure Appl. Math., v. 27, 1974, pp. 25-37. MR 0338594 (49:3358)
  • [8] J. A. KRUPP & J. D. COLE, Studies in Transonic Flow IV, Unsteady Transonic Flow, UCLA Eng. Dept. Rep. No. 76/04, 1976.
  • [9] P. D. LAX & B. WENDROFF, "Systems of conservation laws," Comm. Pure Appl. Math., v. 23, 1960, pp. 217-237. MR 0120774 (22:11523)
  • [10] A. MAJDA & S. OSHER, "Numerical viscosity and the entropy condition," Comm. Pure Appl. Math. (Submitted.) MR 539160 (80j:65031)
  • [11] M. S. MOCK, "Systems of conservation laws of mixed type," J. Differential Equations. (Submitted.) MR 583340 (81m:35088)
  • [12] E. M. MURMAN & J. D. COLE, "Calculations of plane steady transonic flows," AIAA J., v. 9, 1971, pp. 114-121.

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Article copyright: © Copyright 1980 American Mathematical Society

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