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arXiv · 2109.07183

Residual viscosity stabilized RBF-FD methods for solving nonlinear conservation laws

Igor Tominec·Murtazo Nazarov
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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.

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Igor Tominec, Murtazo Nazarov. 2021-09-15. Residual viscosity stabilized RBF-FD methods for solving nonlinear conservation laws. https://arxiv.org/abs/2109.07183

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