@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} }