TY - JOUR
T1 - Schemes with Well-Controlled Dissipation. Hyperbolic Systems in Nonconservative Form
AU - Beljadid , Abdelaziz
AU - G. LeFloch , Philippe
AU - Mishra , Siddhartha
AU - Parés , Carlos
JO - Communications in Computational Physics
VL - 4
SP - 913
EP - 946
PY - 2018
DA - 2018/04
SN - 21
DO - http://doi.org/10.4208/cicp.OA-2016-0019
UR - https://global-sci.org/intro/article_detail/cicp/11266.html
KW - 
AB - <p style="text-align: justify;">We propose here a class of numerical schemes for the approximation of
weak solutions to nonlinear hyperbolic systems in nonconservative form<span style="text-align: justify;">&nbsp;–&nbsp;</span>the notion
of solution being understood in the sense of Dal Maso, LeFloch, and Murat (DLM).
The proposed numerical method falls within LeFloch-Mishra&#39;s framework of schemes
with well-controlled dissipation (WCD), recently introduced for dealing with small-scale
dependent shocks. We design WCD schemes which are consistent with a given
nonconservative system at arbitrarily high-order and then analyze their linear stability.
We then investigate several nonconservative hyperbolic models arising in complex
fluid dynamics, and we numerically demonstrate the convergence of our schemes toward
physically meaningful weak solutions.</p>