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, compressible 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)

  • BibTex
  • RIS
  • TXT
@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} }
TY - JOUR T1 - Fundamentals of Lax-Wendroff Type Approach to Hyperbolic Problems with Discontinuities AU - Li , Jiequan JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 571 EP - 582 PY - 2019 DA - 2019/01 SN - 11 DO - http://doi.org/10.4208/aamm.2018.s02 UR - https://global-sci.org/intro/article_detail/aamm/12981.html KW - Hyperbolic problems, compressible fluid flows, shocks, material interfaces, Lax-Wendroff type methods, generalized Riemann problem (GRP) method. AB -

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.

Jiequan Li. (2019). Fundamentals of Lax-Wendroff Type Approach to Hyperbolic Problems with Discontinuities. Advances in Applied Mathematics and Mechanics. 11 (3). 571-582. doi:10.4208/aamm.2018.s02
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