Radial basis function collocation method for the numerical solution of the two-dimensional transient nonlinear coupled Burgers' equations

摘要

This paper examines the numerical solution of the transient nonlinear coupled Burgers' equations by a Local Radial Basis Functions Collocation Method (LRBFCM) for large values of Reynolds number (Re) up to 10~3. The LRBFCM belongs to a class of truly meshless methods which do not need any underlying mesh but works on a set of uniform or random nodes without any a priori node to node connectivity. The time discretization is performed in an explicit way and collocation with the multiquadric radial basis functions (RBFs) are used to interpolate diffusion-convection variable and its spatial derivatives on decomposed domains. Five nodded domains of influence are used in the local support. Adaptive upwind technique [1,54] is used for stabilization of the method for large Re in the case of mixed boundary conditions. Accuracy of the method is assessed as a function of time and space discretizations. The method is tested on two benchmark problems having Dirich-let and mixed boundary conditions. The numerical solution obtained from the LRBFCM for different value of Re is compared with analytical solution as well as other numerical methods [15,47,49]. It is shown that the proposed method is efficient, accurate and stable for flow with reasonably high Reynolds numbers.