Time-related element-free Taylor-Galerkin method with non-splitting decoupling process for incompressible steady flow

Abstract

The time-related element-free Taylor–Galerkin method with non-splitting decoupling process (EFTG-NSD) is proposed for the simulation of steady flows. The goal of the present paper is twofold. One is to raise the efficiency of the time-related methods for solving steady flow problems, and the other is to obtain a good stability. The EFTG-NSD method, which uses the time-related Navier–Stokes equations to describe steady flows, does not care about the intermediate process and obtains solution of steady flows through time marching. Different from the classical time-related fractional step methods, the EFTG-NSD method decouples the Navier–Stokes equations without any operator-splitting and correction. Because the elimination of correction at each iteration step reduces the computation cost, the EFTG-NSD method possesses higher computation efficiency. In addition, the EFTG-NSD method has a good stability due to the use of the Taylor–Galerkin formula in time and space discretization. Furthermore, the method combining element-free Galerkin method with Taylor–Galerkin method is an important supplement of the element-free Galerkin method for solving flow problems. Copyright © 2011 John Wiley & Sons, Ltd.