A semi-implicit augmented IIM for Navier-Stokes equations with open and traction boundary conditions

In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open and traction boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For this type of problem, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier-Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM so that a fast Poisson solver can be used. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an imcompressible fluid and a compressible gas bubble is also presented. keywords: Navier-Stokes equations, finite difference approximation, irregular domain, open and traction boundary condition, local pressure boundary condition, augmented immersed interface method (IIM). AMS Subject Classification 2000 65M06, 65M85, 76M20.