Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Abgrall. Multiresolution in unstructured meshes: Application to CFD.Numerical methods for fluid dynamics, Oxford University Press5, 1996.
R. Abgrall, S. Lantéri, and T. Sonar. ENO schemes for compressible fluid dynamics.ZAMM Z. angew. Math. Mech.79:3–28, 1999.
F. Arandiga and R. Donat. Nonlinear multiscale decompositions: The approach of A. Harten.Numerical Algorithms23:175–216, 2000.
B.L Bihari and A. Harten. Multiresolution schemes for the numerical solutions of 2D conservation laws.SIAM J. Sci. Comp.18(2):315–354, 1997.
G. Chiavassa and R. Donat. Point Value Multi-scale Algorithms for 2D compressible flows. To appear in Siam J. Sci. Comp., 2001.
W. Dahmen, B. Gottschlich-Müller, and S. Müller. Multiresolution schemes for conservation laws.Technical reportBericht Nr 159 IGMP, RWTH Aachen, 1998.
R. Donat,, J.A. Font, J.M. Ibànez, and A. Marquina. A flux-split algorithm applied to relativistic flows.J. Comput. Phys.146:58–41, 1998.
R. Donat and A. Marquina. Capturing shock reflections: An improved flux formula.J. Comp. Phys.125, 1996.
R. Fedkiw, B. Merriman, R. Donat, and S. Osher.The penultimate scheme for systems of conservation laws: Finite difference ENO with Marquina’s flux splitting. UCLA CAM Report, January 1997.
A. Harten. Discrete multiresolution analysis and generalized wavelets.J. Appl. Nu-mer. Math.12:153–192, 1993.
A. Harten. Multiresolution algorithms for the numerical solution of hyperbolic conservation laws.Comm. Pure Appl. Math.48, No 12, 1995.
S.M. Kaber and M. Postel. Finite volume schemes on triangles coupled with multiresolution analysis.C.R. Acad. Sci., Série I, Paris328:817–822, 1999.
P. D. Lax and X.-D. Liu. Solution of two-dimensional Riemann problems of gas dynamics by positive schemes.SIAM J. Sci. Comput.19:319–340, 1998.
C.W. Schulz-Rinne. Classification of the Riemann problem for two-dimensional gas dynamics.SIAM J. Math Anal.24:76–88, 1993.
C.W. Schulz-Rinne, J. P. Collins, and H. M. Glaz. Numerical solution of the Riemann problem for two-dimensional gas dynamics.SIAM J. Sci. Comput.14:1394–1414, 1993.
C. W Shu and S. J. Osher. Efficient implementation of essentially non-oscillatory shock-capturing schemes II.J. Comp. Phys.83, 1989.
B. Sjögreen. Numerical experiments with the multiresolution scheme for the compressible euler equations.J. Comp. Phys.117, 1995.
T. Zhang, G.-Q. Chen, and Y. Yang. On the 2D Riemann problem for the compressible Euler equations, I. interaction of shocks and rarefaction waves.Discrete Continous Dynam. Systems1:555–584, 1995.
T. Zhang and Y. Zheng. Conjecture on the structure of solutions of the Riemann problem for two-dimensional gas dynamics systems.SIAM J. Math Anal.21:593–630, 1990.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Basel AG
About this paper
Cite this paper
Chiavassa, G., Donat, R., Marquina, A. (2001). Fine-Mesh Numerical Simulations for 2D Riemann Problems with a Multilevel Scheme. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 140. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8370-2_26
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8370-2_26
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9537-8
Online ISBN: 978-3-0348-8370-2
eBook Packages: Springer Book Archive