Numerical simulation of incompressible viscous flow in deforming domains

We present a second-order accurate finite difference method for numerical s olution of the incompressible Navier-Stokes equations in deforming domains. Our approach is a generalization of the Bell-Colella-Glaz predictor-correc tor method for incompressible flow. In order to treat the time-dependence a nd inhomogeneities in the incompressibility constraint introduced by presen ce of deforming boundaries, we introduce a nontrivial splitting of the velo city field into vortical and potential components to eliminate the inhomoge neous terms in the constraint and a generalization of the Bell-Colella-Glaz algorithm to treat time-dependent constraints. The method is second-order accurate in space and time, has a time step constraint determined by the ad vective Colella-Friedrichs-Lewy condition, and requires the solution of wel l behaved linear systems amenable to the use of fast iterative methods. We demonstrate the method on the specific example of viscous incompressible fl ow in an axisymmetric deforming tube.