TY - JOUR
T1 - Relaxation Schemes for Entropy Dissipative Systems of Viscous Conservation Laws
AU - Chen , Tuowei
AU - Li , Jiequan
JO - Communications in Computational Physics
VL - 4
SP - 953
EP - 986
PY - 2025
DA - 2025/09
SN - 38
DO - http://doi.org/10.4208/cicp.OA-2024-0299
UR - https://global-sci.org/intro/article_detail/cicp/24350.html
KW - Relaxation method, viscous conservation laws, entropy dissipation, Lax-Wendroff type solver, Navier-Stokes equations, generalized Riemann problem.
AB - <p style="text-align: justify;">In this paper, a hyperbolic relaxation model is designed for a class of entropy dissipative systems of viscous conservation laws, such as the 1-D viscous Burgers and 2-D Navier-Stokes equations. An artificial variable is introduced to relax both
the convective and viscous fluxes together. Based on the entropy dissipative property of the original system, a dissipation condition is proposed for the resulting relaxation model, and used to prove the entropy inequality of the relaxation model for
linear convection-diffusion equations. Lax-Wendroff type second-order finite-volume
schemes are developed to discretize the relaxation model. A number of numerical experiments, including viscous compressible flow problems from subsonic to supersonic
speeds, are used to validate the relaxation model and evaluate the performance of the
current schemes.</p>