Slope limiters for radial basis functions applied to conservation laws with discontinuous flux function

Abstract

We present slope limiters in meshless radial basis functions for solving nonlinear equations of conservation laws with flux function that depends on discontinuous coefficients. The method is based on the local collocation formulation and does not require either generation of a grid or evaluation of an integral. Upwind techniques are used to allocate collocation points within the characteristic solutions and different slope limiter functions are investigated. The main advantages of this approach are neither mesh generations nor Riemann problem solvers are required during the solution process. Numerical results are shown for several test examples including models on vehicular traffic and two-phase flows. The main focus is to examine the performance of the proposed meshless method for shock-capturing property in conservation laws with discontinuous flux function. The obtained results demonstrate its ability to capture the main solution features.