Application of the method of fundamental solutions and the radial basis functions for viscous laminar flow in wavy channel

Abstract

This paper deals with the problem of viscous laminar flow in a wavy channel using the method of fundamental solutions and the radial basis functions. First approximation was obtained when the Reynolds number equals zero, in which the considered problem is homogeneous problem which can be easily solved using the method of fundamental solutions. In order to obtain subsequent approximations of the solution, the nonlinear problem was transformed into a sequence of inhomogeneous problems using the Picard iteration method. Applying the method of particular solutions on each iteration step the solution consists of the general solution and the particular solution. The right-hand side of the governing equation in subsequent iteration steps was interpolated using the radial basis functions. Simultaneously the particular solution was obtained and the general solution was obtained by means of the method of fundamental solutions. The unknown coefficients of the solution were obtained using the boundary collocation technique. The main advantage of the proposed procedure is its simplicity and analytical form of the approximate solution. Such meshless approach was never applied previously for the problem of viscous laminar flow in the wavy channel.