A stabilized RBF finite difference method for convection dominated flows over meshfree nodes

Abstract

In this paper, a stabilized solution scheme is presented for solving highly convective flow equations on meshfree nodal distribution. The stabilized terms are obtained by considering higher order approximation of governing differential equations over finite control volume while applying force and momentum balance. Spatial derivatives, of resulting flow equations, are treated with Radial Basis Functions in Finite Difference Method (RBF-FD) over meshfree nodal cloud. The characteristic length, for applying equilibrium of forces and momentum, is proposed to be a function of Reynolds number and flow velocity. Performance and accuracy of the proposed scheme is tested for 1-D Convection-Diffusion equations. Numerical tests are conducted for initial conditions having step as well as uniformly varying field variables. The scheme is found to be effective in suppressing the non-physical numerical fluctuations associated with convection dominated flows. Accuracy of the solution with stabilized term is found to be higher than the one without stabilization. The solution scheme is also used for flow around static NACA0012 airfoil at Re=10,000. The stabilization term is found to effectively suppress the numerical oscillation when compared to non-stabilized scheme.