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 - <p style="text-align: justify;">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.</p>