A projection method for incompressible viscous flow on moving quadrilateral grids

We present a second-order accurate projection method for numerical solution of the incompressible Navier-Stokes equations on moving quadrilateral grids. Our approach is a generalization of the Bell-Colella-Glaz (BCG) predictor-corrector method for incompressible flow. Irregular geometry is represented in terms of a moving, body-fitted cylindrical coordinate system. Mapped coordinates are used to smoothly transform in both time and space the moving domain onto a logically rectangular domain which is fixed in time. To treat the time dependence and inhomogeneities in the incompressibility constraint introduced by the presence of deforming boundaries. wt: introduce a nontrivial splitting of the velocity held into vortical and potential components to eliminate the inhomogeneous terms in the constraint and a generalization of the BCG algorithm to treat time-dependent constraints. The method is second-order accurate in space and time. has a time step constraint determined by the advective CFL condition, and requires the solution of well-behaved linear systems amenable to the use of fast iterative methods. We demonstrate the method on the specific example of viscous incompressible flow in an axisymmetric deforming tube. (C) 2001 Academic Press.