Abstract
AbstractIn 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.
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,General Engineering,Theoretical Computer Science,Software,Applied Mathematics,Computational Mathematics,Numerical Analysis
Reference29 articles.
1. Barnett, G.A.: A robust RBF-FD formulation based on polyharmonic splines and polynomials. Ph.D. thesis, University of Colorado at Boulder, Dept. of Applied Mathematics, Boulder, CO, USA (2015)
2. Bayona, V.: An insight into RBF-FD approximations augmented with polynomials. Comput. Math. Appl. 77, 2337–2353 (2019). https://doi.org/10.1016/j.camwa.2018.12.029
3. Bayona, V., Flyer, N., Fornberg, B., Barnett, G.A.: On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs. J. Comput. Phys. 332, 257–273 (2017). https://doi.org/10.1016/j.jcp.2016.12.008
4. Flyer, N., Fornberg, B., Bayona, V., Barnett, G.A.: On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy. J. Comput. Phys. 321, 21–38 (2016). https://doi.org/10.1016/j.jcp.2016.05.026
5. Flyer, N., Lehto, E., Blaise, S., Wright, G.B., St-Cyr, A.: A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere. J. Comput. Phys. 231(11), 4078–4095 (2012). https://doi.org/10.1016/j.jcp.2012.01.028
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献