An Unconditionally Stable Method for the Euler Equations

Journal of Computational Physics

Volumn 150, Issue 1, 1999, Pages 76-96

  Holden, Helge ^a   Lie, Knut Andreas ^a   Risebro, Nils Henrik ^b  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^b UNIVERSITY OF OSLO   (Norway)

Author keywords

Dimensional splitting; Euler equations; Front tracking; Grid refinement

Indexed keywords

GAS DYNAMICS; WIND TUNNELS;

ADAPTIVE GRID REFINEMENT; DIMENSIONAL SPLITTING; EULER'S EQUATION; FRONT TRACKING; FRONT TRACKING METHOD; GRID REFINEMENT; SPACE DIMENSIONS; SPLITTINGS; SYSTEMS OF CONSERVATION LAWS; UNCONDITIONALLY STABLE METHODS;

EULER EQUATIONS;

EID: 0041935750     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.6164     Document Type: Article

References (30)

1. Arora M., Roe P. L. On postshock oscillations due to shock capturing schemes in unsteady flows. J. Comput. Phys. 130:1997;25.
2. Baiti P., Jenssen H. K. On the front tracking algorithm. J. Math. Anal. Appl. 217:1998;395.
3. Bratvedt F., Bratvedt K., Buchholz C. F., Gimse T., Holden H., Holden L., Risebro N. H. Frontline and Frontsim, two full scale, two-phase, black oil reservoir simulators based on front tracking. Surv. Math. Ind. 3:1993;185.
4. A. Bressan, G. Crasta, B. Piccoli, Well-posedness of the Cauchy problem fornn, Mem. Am. Math. Soc.
5. Bressan A., LeFloch P. Uniqueness of weak solutions to systems of conservation laws. Arch. Rational Mech. Anal. 140:1997;301.
6. Chern I.-L., Glimm J., McBryan O., Plohr B., Yaniv S. Front tracking for gas dynamics. J. Comput. Phys. 62:1986;83.
7. Chorin A. J. Random choice solutions of hyperbolic systems. J. Comput. Phys. 22:1976;517.
8. Colella P. An Analysis of the Effect of Operator Splitting and of the Sampling Procedure on the Accuracy of Glimm's Method. 1979.
9. Colella P. Glimm's method for gas dynamics. SIAM J. Sci. Statist. Comput. 3:1982;76.
10. Glimm J. Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18:1965;697.
11. Gottlieb J. J., Groth C. P. T. Assessment of Riemann solvers for unsteady one-dimensional inviscid flows of perfect gases. J. Comput. Phys. 78:1988;437.
12. Holdahl R. Front Tracking for the Shallow Water Equations. 1998.
13. R. Holdahl, H. Holden, K.-A. Lie, Unconditionally stable splitting methods for the shallow water equations, BIT.
14. H. Holden, N. H. Risebro, Front tracking for conservation laws, Department of Mathematics, Norwegian University of Science and Technology.
15. Holden H., Risebro N. H. A method of fractional steps for scalar conservation laws without the CFL condition. Math. Comp. 60:1993;221.
16. Jiang G.-S., Tadmor E. Non-oscillatory central schemes for multidimensional hyperbolic conservation laws. SIAM J. Sci. Comput. 19:1998;1892.
17. Langseth J. O. On an implementation of a front tracking method for hyperbolic conservation laws. Adv. Engrg. Software. 26:1996;45.
18. J. O. Langseth, R. J. LeVeque, A wave propagation method for three-dimensional hyperbolic conservation laws, www.math.ntnu.no/conservation/.
19. Langseth J. O., Risebro N. H., Tveito A. A conservative front tracking scheme for 1D hyperbolic conservation laws. Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects. 43:1993;385.
20. R. J. LeVeque, clawpack, netlib.att.com at netlib/pdes/claw/ or at www.amath. washington.edu/~rjl/clawpack.html.
21. LeVeque R. J. A large time step generalization of Godunov's method for systems of conservation laws. SIAM J. Numer. Anal. 22:1985;1051.
22. Lie K.-A., Haugse V., Karlsen K. H. Dimensional splitting with front tracking and adaptive grid refinement. Numer. Methods Partial Differential Equations. 14:1998;627.
23. J. J. Quirk, Godunov-type schemes applied to detonation flows, Combustion in High-Speed Flows, J. Buckmaster, et al., 575, Kluwer, Dordrecht, 1994.
24. Quirk J. J. A contribution to the great Riemann solver debate. Internat. J. Numer. Methods Fluids. 18:1994;555.
25. Risebro N. H. A front-tracking alternative to the random choice method. Proc. Am. Math. Soc. 117:1993;1125.
26. Risebro N. H., Tveito A. Front tracking applied to a nonstrictly hyperbolic system of conservation laws. SIAM J. Sci. Statist. Comput. 12:1991;1401.
27. Risebro N. H., Tveito A. A front tracking method for conservation laws in one dimension. J. Comput. Phys. 101:1992;130.
28. Toro E. F. Riemann Solvers and Numerical Methods for Fluid Dynamics. 1997.
29. Woodward P., Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54:1984;115.
30. K. Xu, Gas evolution dynamics in Godunov-type schemes, www.math.ntnu.no/conservation/.