A projection method for solving incompressible viscous flows on domains with moving boundaries

Abstract

In this paper, a projection method is presented for solving the flow problems in domains with moving boundaries. In order to track the movement of the domain boundaries, arbitrary-Lagrangian-Eulerian (ALE) co-ordinates are used. The unsteady incompressible Navier-Stokes equations on the ALE coordinates are solved by using a projection method developed in this paper. This projection method is based on the Bell's Godunov-projection method. However, substantial changes are made so that this algorithm is capable of solving the ALE form of incompressible Navier-Stokes equations. Multi-block structured grids are used to discretize the flow domains. The grid velocity is not explicitly computed; instead the volume change is used to account for the effect of grid movement. A new method is also proposed to compute the freestream capturing metrics so that the geometric conservation law (GCL) can be satisfied exactly in this algorithm. This projection method is also parallelized so that the state of the art high performance computers can be used to match the computation cost associated with the moving grid calculations. Several test cases are solved to verify the performance of this moving-grid projection method. © 2004 John Wiley and Sons, Ltd.