Transmission of a Slowly Moving Shock across a Nonconservative Interface

Journal of Computational Physics

Volumn 171, Issue 2, 2001, Pages 579-615

  Wu, Zi Niu ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Nonconservative grid interface; Shock interface transmission; Slowly moving shock; Two shocked solution

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; GAS DYNAMICS; INTERFACE STATES; MESH GENERATION; PARTIAL DIFFERENTIAL EQUATIONS; PHASE INTERFACES;

DIFFERENCE SCHEMES; GRID INTERFACES; MESH SIZE; NONCONSERVATIVE; NONCONSERVATIVE GRID INTERFACE; OVERLAPPING GRIDS; SHOCK-WAVES; SHOCK/INTERFACE TRANSMISSION; SLOWLY MOVING SHOCK; TWO-SHOCKED SOLUTION;

SHOCK WAVES;

EID: 0012875803     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2001.6797     Document Type: Article

References (39)

1. Abgrall R. How to prevent pressure oscillations in multicomponent flow calculations: A quasi conservative approach. J. Comput. Phys. 125:1996;150.
2. Allen C. B. The reduction of numerical entropy generated by unsteady shock waves. Aeronaut. J. 101:1997;9.
3. Arora M., Roe P. L. On postshock oscillations due to shock capturing schemes in unsteady flows. J. Comput. Phys. 130:1997;25.
4. Axel R. M., Newtown P. K. The interaction of shocks with dispersive waves-II. Incompressible-integrable limit. Stud. Appl. Math. 100:1998;311.
5. Berger M. On conservation at grid interfaces. SIAM J. Numer. Anal. 24:1987;967.
6. Chesshire G., Henshaw D. Composite overlapping meshes for the solution of partial differential equations. J. Comput. Phys. 90:1990;1.
7. Chesshire G., Henshaw D. A scheme for conservative interpolation on overlapping grids. SIAM J. Sci. Comput. 15:1994;819.
8. Engquist B., Gustafsson B. Steady-state computations for wave propagation problems. Math. Comput. 49:1987;39.
9. Fedkiw R. P., Aslam T., Merriman B., Osher S. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the Ghost Fluid Method). J. Comput. Phys. 152:1999;457.
10. Gustafsson B. The Euler and Navier-Stokes equations. Wellposedness, stability and composite grids. Computational Fluid Dynamics. 1991;1991-2001.
11. Hirsch C. Numerical Computation of Internal and External Flows. 1 and 2:1990.
12. Jin S., Liu J. G. The effect of numerical viscosities. I. Slowly moving shocks. J. Comput. Phys. 126:1996;373.
13. Karni S. Multi-component flow calculations by a consistent primitive algorithm. J. Comput. Phys. 112:1994;31.
14. Karni S. Hybrid multifluid algorithms. SIAM J. Sci. Comput. 17:1996;1019.
15. Karni S., Canic S. Computations of slowly moving shocks. J. Comput. Phys. 136:1997;132.
16. Kreiss H.-O., Lorenz J. Initial-Boundary Value Problems and the Navier-Stokes Equations. 1989.
17. Lax P., Wendroff B. System of conservation laws. Comm. Pure Appl. Math. XIII:1960;217.
18. Lin W. C. Dissipation additions to flux difference splitting. J. Comput. Phys. 117:1995;20.
19. Lin W. C. Hyperbolic conservation laws with a moving source. Comm. Pure Appl. Math. 52:1999;1075.
20. Liou M. S. A sequel to AUSM: AUSM(+). J. Comput. Phys. 129:1996;364.
21. Meadows K. R., Caughey D. A., Casper J. Computing unsteady shockwaves for aeroacoustic applications. AIAA J. 32:1994;1360.
22. Olsson F. R., Pertersson N. A. Stability of interpolation on overlapping grids. Comput. Fluids. 25:1996;583.
23. Osher S. Riemann solvers, the entropy condition and difference approximations. SIAM J. Numer. Anal. 21:1984;217.
24. Pärt E., Sjögreen B. Shock Waves and Overlapping Grids. 1991.
25. Pärt-Enander E., Sjögreen B. Conservative and non-conservative interpolation between overlapping grids for finite volume solutions of hyperbolic problems. Comput. Fluids. 23:1994;551.
26. Parter S. V. On the overlapping grid method for elliptic boundary-value problems. SIAM J. Numer. Anal. 36:1999;819.
27. Roberts T. W. The behavior of flux difference splitting schemes near slowly moving shock waves. J. Comput. Phys. 90:1990;141.
28. Roe P. L. Approximate Riemann solvers: Parameter vector and difference schemes. J. Comput. Phys. 43:1981;357.
29. Starius G. On composite mesh difference methods for hyperbolic differential equations. Numer. Math. 35:1980;241.
30. Tadmor E. Numerical viscosity and the entropy condition for conservative difference schemes. Math. Comput. 43:1984;369.
31. Tang H. S., Zhou T. On nonconservative algorithms for grid interfaces. SIAM J. Numer. Anal. 37:1999;173.
32. Thuné M. Stability of Difference Approximations of Hyperbolic Systems on Substructured Domains. 1986.
33. Wang Z. J. A fully conservative interface algorithm for overlapping grids. J. Comput. Phys. 122:1995;96.
34. Wu Z. N. Uniqueness of steady state solutions for difference equations on overlapping grids. SIAM J. Numer. Anal. 33:1996;1336.
35. Wu Z. N. Convergence study of an implicit multidomain method for compressible flow computations. Comput. Fluids. 25:1996;181.
36. Wu Z. N. Steady and unsteady shock waves on overlapping grids. SIAM J. Sci. Comput. 20:1999;1850.
37. Wu Z. N., Zou H. Grid overlapping for implicit parallel computations of compressible flows. J. Comput. Phys. 157:2000;2.
38. Z. N. Wu, Slowly moving shock waves for the Euler equations in gas dynamics, submitted for publication.
39. Xu K., Hu J. S. Projection dynamics in Godunov-type schemes. J. Comput. Phys. 142:1998;412.