Fine-Mesh Numerical Simulations for 2D Riemann Problems with a Multilevel Scheme

The numerical simulation of physical problems modeled by systems of conservation laws can be difficult due to the occurrence of discontinuities and other non-smooth features in the solution.

[1]  James P. Collins,et al.  Numerical Solution of the Riemann Problem for Two-Dimensional Gas Dynamics , 1993, SIAM J. Sci. Comput..

[2]  C. Schulz-Rinne,et al.  Classification of the Riemann problem for two-dimensional gas dynamics , 1991 .

[3]  Rosa Donat,et al.  A Flux-Split Algorithm applied to Relativistic Flows , 1998 .

[4]  Barna L. Bihari,et al.  Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I , 1997, SIAM J. Sci. Comput..

[5]  A. Harti.  Discrete multi-resolution analysis and generalized wavelets , 1993 .

[6]  Sidi Mahmoud Kaber,et al.  Finite volume schemes on triangles coupled with multiresolution analysis , 1999 .

[7]  Xu-Dong Liu,et al.  Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes , 1998, SIAM J. Sci. Comput..

[8]  R. Abgrall,et al.  ENO approximations for compressible fluid dynamics , 1999 .

[9]  Tong Zhang,et al.  Conjecture on the structure of solutions of the Riemann problem for two-dimensional gas dynamics systems , 1990 .

[10]  Antonio Marquina,et al.  Capturing Shock Reflections , 1996 .

[11]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[12]  Rosa Donat,et al.  Point Value Multiscale Algorithms for 2D Compressible Flows , 2001, SIAM J. Sci. Comput..

[13]  Wolfgang Dahmen,et al.  Multiresolution schemes for conservation laws , 2001 .

[14]  Gui-Qiang Chen,et al.  On the 2-D Riemann problem for the compressible Euler equationsI. Interaction of shocks and rarefaction waves , 1995 .

[15]  Björn Sjögreen,et al.  Numerical experiments with the multiresolution scheme for the compressible Euler equations , 1995 .