A completely explicit scheme of Cauchy problem in BSLM for solving the Navier-Stokes equations

摘要

This paper presents a backward semi-Lagrangian method (BSLM) with third-order convergence in both time and space for solving incompressible Navier-Stokes equations. The third-order backward differentiation formula for the total time derivative and the projection method for the steady-state Stokes equation are used. A fourth-order difference scheme together with a local bi-cubic interpolation is used to solve the resulted two governing equations for the velocity and pressure. This paper mainly focuses on the development of an efficient scheme for solving the nonlinear Cauchy problem of the characteristic curve. We employ a modified linear multi-step method of the implicit-type based on the error correction strategy. A novel contribution of this paper is the design of a completely explicit formula for the three foot-points. The proposed method is superior to existing methods in terms of computational costs and accuracy, allowing the use of a large time step size. The fully explicit formula for the foot-points significantly improves the performance of a common BSLM for a wide range of practical applications. (C) 2019 Elsevier Inc. All rights reserved.