@Article{CiCP-38-953,
author = {Chen , Tuowei and Li , Jiequan},
title = {Relaxation Schemes for Entropy Dissipative Systems of Viscous Conservation Laws},
journal = {Communications in Computational Physics},
year = {2025},
volume = {38},
number = {4},
pages = {953--986},
abstract = {<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>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2024-0299},
url = {http://global-sci.org/intro/article_detail/cicp/24350.html}
}