A stencil adaptive algorithm for finite difference solution of incompressible viscous flows

In this paper, a solution-adaptive algorithm is presented for the simulation of incompressible viscous flows. The framework of this method consists of an adaptive local stencil refinement algorithm and 3-points central difference discretization. The adaptive local stencil refinement is designed in such a manner that 5-points symmetric stencil is guaranteed at each interior node, so that conventional finite difference formula can be easily constructed everywhere in the domain. Thus, high efficiency and accuracy of central difference scheme can be ultimately enjoyed together with the solution-adaptive property. The adaptive finite difference method has been tested by three numerical examples, to examine its performance in the twodimensional problems. The numerical examples include Poisson equation, moving interface problem and a lid-driven incompressible flow problem. It was found that the multigrid approach can be efficiently combined with solution-adaptive algorithm to speed up the convergence rate. 2005 Elsevier Inc. All rights reserved.