  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.
