Upwind skewed radial basis functions (USRBF) for solution of highly convective problems over meshfree nodes

Abstract

An upwind skewed radial basis function (USRBF)-based solution scheme is presented for stabilized solutions of convection-dominated problems over meshfree nodes. The conventional, radially symmetric radial basis functions (RBFs) are multiplied with an upwinding factor which skews the RBFs toward the upwind direction. The upwinding factor is a function of flow direction, intensity of convection, size of local support domain, and nodal distribution. The use of USRBFs modifies the weight values such that the necessary artificial diffusion is added only along the flow direction, whereas the crosswind diffusion is avoided. Subsequently, these skewed radial basis functions are employed in finite difference mode (RBF-FD) for derivative approximation. The performance and accuracy of the proposed scheme is studied by solving convection–diffusion problems over uniform and random distribution of meshfree nodes with various convection intensities. The upwinding effectively suppresses non-physical perturbation in numerical solution of convection-dominated problems. The results show that significant improvement in accuracy can be achieved by using the proposed USRBF-based solution scheme, particularly at higher convection intensities.