TY - JOUR
T1 - Multidimensional Relaxation Approximations for Hyperbolic Systems of Conservation Laws
AU - Seaïd , Mohammed
JO - Journal of Computational Mathematics
VL - 4
SP - 440
EP - 457
PY - 2007
DA - 2007/08
SN - 25
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8703.html
KW - Multidimensional hyperbolic systems, Relaxation methods, Non-oscillatory
reconstructions, Asymptotic-preserving schemes.
AB - <p style="text-align: justify;">We construct and implement a non-oscillatory relaxation scheme for multidimensional hyperbolic systems of conservation laws. The method transforms the nonlinear hyperbolic system to a semilinear model with a relaxation source term and linear characteristics which can be solved numerically without using either Riemann solver or linear iterations. To discretize the relaxation system we consider a high-resolution reconstruction in space and a TVD Runge-Kutta time integration. Detailed formulation of the scheme is given for problems in three space dimensions and numerical experiments are implemented in both scalar and system cases to show the effectiveness of the method.</p>