Residual viscosity stabilized RBF-FD methods for solving nonlinear conservation laws
Abstract
In this paper, we solve nonlinear conservation laws using the radial basis function generated finite difference (RBF-FD) method. Nonlinear conservation laws have solutions that entail strong discontinuities and shocks, which give rise to numerical instabilities when the solution is approximated by a numerical method. We introduce a residual-based artificial viscosity (RV) stabilization framework adjusted to the RBF-FD method, where the residual of the conservation law adaptively locates discontinuities and shocks. The RV stabilization framework is applied to the collocation RBF-FD method and the oversampled RBF-FD method. Computational tests confirm that the stabilized methods are reliable and accurate in solving scalar conservation laws and conservation law systems such as compressible Euler equations.
Keywords
Cite
@article{arxiv.2109.07183,
title = {Residual viscosity stabilized RBF-FD methods for solving nonlinear conservation laws},
author = {Igor Tominec and Murtazo Nazarov},
journal= {arXiv preprint arXiv:2109.07183},
year = {2022}
}