An Upwind Scheme to Solve Unsteady Convection-Diffusion Equations Using Radial Basis Function Based Local Hermitian Interpolation Method with PDE Centres

Spurious oscillations occur in the numerical results of convective dominated problems with discontinuities when central interpo- lation schemes are used. Upwind interpolation is necessary to overcome these oscillations. In this work, an upwind scheme is proposed to solve the unsteady convection-diffusion equation using Radial Basis Function (RBF) based Local Hermitian Interpo- lation (LHI) with PDE centres. It is a meshless numerical method based on the interpolation of overlapping RBF systems and also satisfy the governing partial differential equations at certain specified locations. Local hermite interpolation gives symmetric non-singular interpolation matrix which can be inverted easily to solve the system of equations. The scheme is implemented to unsteady benchmark problems and validated against the corresponding analytical solutions. Comparisons with the benchmark solutions show that the proposed upwind scheme is stable and produces significantly accurate results especially for convection dominated problems.