Second order front tracking for the Euler equations

Journal of Computational Physics

Volumn 229, Issue 7, 2010, Pages 2719-2739

  Witteveen, Jeroen A S ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Blast waves problem; Hyperbolic conservation laws; Piecewise linear approximation; Riemann problem; Supersonic airfoil flow

Indexed keywords

AIRFOILS; LINEARIZATION; PARTIAL DIFFERENTIAL EQUATIONS; PIECEWISE LINEAR TECHNIQUES;

AIRFOIL FLOWS; BLAST WAVE PROBLEM; BLAST WAVES; FRONT TRACKING; FRONT TRACKING METHOD; HYPERBOLIC CONSERVATION LAWS; PIECEWISE LINEAR APPROXIMATIONS; RIEMANN PROBLEM; SUPERSONIC AIRFOIL FLOW; WAVE PROBLEMS;

EULER EQUATIONS;

EID: 74449088134     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.12.019     Document Type: Article

References (33)

1. Baiti P., and Jenssen H.K. On the front tracking algorithm. J. Math. Anal. Appl. 217 (1998) 395-404
2. Bressan A., and LeFloch P. Uniqueness of weak solution to systems of conservation laws. Arch. Rational Mech. Anal. 140 (1997) 301-317
3. Charrier P., and Tessieras B. On front-tracking methods applied to hyperbolic systems of nonlinear conservation laws. SIAM J. Numer. Anal. 23 (1986) 461-472
4. Chern I.-L., Glimm J., McBryan O., Plohr B., and Yaniv S. Front tracking for gas dynamics. J. Comput. Phys. 62 (1986) 83-110
5. I.-L. Chern, P. Colella, A conservative front tracking method for hyperbolic conservation laws, Technical Report UCRL JC-97200, Lawrence Livermore National Laboratory, 1987.
6. Chern I.-L. Stability theorem and truncation error analysis for the Glimm scheme and for a front tracking method for flows with strong discontinuities. Commun. Pure Appl. Math. 42 (1989) 815-844
7. Chorin A.J., and Marsden J.E. A Mathematical Introduction to Fluid Mechanics (1979), Springer-Verlag, New York
8. Emanuel G. Analytical Fluid Dynamics (2001), CRC Press, Boca Raton
9. Glimm J., Isaacson E., Marchesin D., and McBryan O. Front tracking for hyperbolic systems. Adv. Appl. Math. 2 (1981) 91-119
10. Glimm J. The interaction of nonlinear hyperbolic waves. Commun. Pure Appl. Math. 41 (1988) 569-590
11. Glimm J., Grove J.W., Li X.L., Shyue K.-M., Zeng Y., and Zhang Q. Three-dimensional front tracking. SIAM J. Sci. Comput. 19 (1998) 703-727
12. Glimm J., Li X.L., Liu Y., and Zhao N. Conservative front tracking and level set algorithms. Proc. Natl. Acad. Sci. USA 25 (2001) 14198-14201
13. Holdahl R., Holden H., and Lie K.-A. Unconditionally stable splitting methods for the shallow water equations. BIT 39 (1999) 451-472
14. Holden H., Lie K.-A., and Risebro N.H. An unconditionally stable method for the Euler equations. J. Comput. Phys. 150 (1999) 76-96
15. Holden H., and Risebro N.H. Front Tracking for Hyperbolic Conservation Laws (2002), Springer-Verlag, New York
16. Moretti G. Computations of flows with shocks. Ann. Rev. Fluid Mech. 19 (1987) 313-337
17. Laforest M. Mechanisms for error propagation and cancellation in Glimm's scheme without rarefractions. J. Hyperbol. Differ. Eq. 4 (2007) 501-531
18. Langseth J.O., Risebro N.H., and Tveito A. A conservative front tracking scheme for 1D hyperbolic conservation laws. In: Donato A., et al. (Ed). Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects. Notes on Numerical Fluid Mechanics vol. 43 (1993), Vieweg, Braunschweig 385-392
19. Lie K.-A., Haugse V., and Hvistendahl Karlsen K. Dimensional splitting with front tracking and adaptive grid refinement. Numer. Meth. Part Differ. Eq. 14 (1998) 627-648
20. Liepmann H.W., and Roshko A. Elements of Gasdynamics (1957), Wiley, New York
21. Lucier B.J. A moving mesh numerical method for hyperbolic conservation laws. Math. Comput. 173 (1986) 59-69
22. Raffel M., Willert C., and Kompenhans J. Particle Image Velocimetry: A Practical Guide (1998), Springer Verlag, Berlin
23. Richtmyer R., and Morton K. Difference Methods for Initial Value Problems (1967), Interscience, New York
24. Risebro N.H., and Tveito A. Front tracking applied to a nonstrictly hyperbolic system of conservation laws. SIAM J. Sci. Stat. Comput. 12 (1991) 1401-1419
25. Risebro N.H., and Tveito A. A front tracking method for conservation laws in one dimension. J. Comput. Phys. 101 (1992) 130-139
26. Sod G.A. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27 (1978) 1-31
27. L.J. Souverein, B.W. van Oudheusden, F. Scarano, Particle image velocimetry based loads determination in supersonic flows, in: 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada (2007) AIAA-2007-50.
28. Swartz B.K., and Wendroff B. AZTEC: a front tracking code based on Godunov's method. Appl. Numer. Math. 2 (1986) 385-388
29. Toro E.F. Riemann Solvers and Numerical Methods for Fluid Dynamics (1997), Springer Verlag, Berlin
30. J.A.S. Witteveen, A second-order front tracking method applied to the Euler equations, in: 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada (2006) AIAA-2006-1277.
31. Witteveen J.A.S., Koren B., and Bakker P.G. An improved front tracking method for the Euler equations. J. Comput. Phys. 224 (2007) 712-728
32. Woodward P.R. Trade-offs in designing explicit hydrodynamics schemes for vector computers. In: Rodrigue G. (Ed). Parallel Computation (1982), Academic Press, New York
33. Woodward P.R., and Colella P. The numerical simulation of two-dimensional flow with strong shocks. J. Comput. Phys. 54 (1984) 115-173