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 grid s. Our approach is a generalization of the Bell-Colella-Glaz (BCG) predicto r-corrector method for incompressible flow. Irregular geometry is represent ed in terms of a moving, body-fitted cylindrical coordinate system. Mapped coordinates are used to smoothly transform in both time and space the movin g domain onto a logically rectangular domain which is fixed in time. To tre at the time dependence and inhomogeneities in the incompressibility constra int introduced by the presence of deforming boundaries. wt: introduce a non trivial splitting of the velocity held into vortical and potential componen ts to eliminate the inhomogeneous terms in the constraint and a generalizat ion of the BCG algorithm to treat time-dependent constraints. The method is second-order accurate in space and time. has a time step constraint determ ined by the advective CFL condition, and requires the solution of well-beha ved linear systems amenable to the use of fast iterative methods. We demons trate the method on the specific example of viscous incompressible flow in an axisymmetric deforming tube. (C) 2001 Academic Press.