Volume 11, Issue 3
Fundamentals of Lax-Wendroff Type Approach to Hyperbolic Problems with Discontinuities

Jiequan Li

Adv. Appl. Math. Mech., 11 (2019), pp. 571-582.

Published online: 2019-01

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  • Abstract

This paper presents the understanding of the fundamentals when  designing a numerical schemes for hyperbolic problems with discontinuities as parts of their solutions. The fundamentals include the consistency with hyperbolic balance laws in integral form rather than PDE form, spatial-temporal coupling, thermodynamic consistency for computing compressible fluid flows,  convergence arguments and multidimensionality etc.  Some numerical results are shown to display the performance.

  • Keywords

Hyperbolic problems, ccmpressible fluid flows, shocks, material interfaces, Lax-Wendroff type methods, generalized Riemann problem (GRP) method.

  • AMS Subject Headings

35L65, 65M08, 65N08, 76N15, 76T10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

li jiequan@iapcm.ac.cn (Jiequan Li)

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@Article{AAMM-11-571, author = {Li , Jiequan }, title = {Fundamentals of Lax-Wendroff Type Approach to Hyperbolic Problems with Discontinuities}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {3}, pages = {571--582}, abstract = {

This paper presents the understanding of the fundamentals when  designing a numerical schemes for hyperbolic problems with discontinuities as parts of their solutions. The fundamentals include the consistency with hyperbolic balance laws in integral form rather than PDE form, spatial-temporal coupling, thermodynamic consistency for computing compressible fluid flows,  convergence arguments and multidimensionality etc.  Some numerical results are shown to display the performance.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2018.s02}, url = {http://global-sci.org/intro/article_detail/aamm/12981.html} }
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