A Simple 3D Immersed Interface Method for Stokes Flow with Singular Forces on Staggered Grids

Abstract

In this paper, a fairly simple 3D immersed interface method based on the CG-Uzawa type method and the level set representation of the interface is employed for solving three-dimensional Stokes flow with singular forces along the interface. The method is to apply the Taylor's expansions only along the normal direction and incorporate the jump conditions up to the second normal derivatives into the finite difference schemes. A second order geometric iteration algorithm is employed for computing orthogonal projections on the surface with third-order accuracy. The Stokes equations are discretized involving the correction terms on staggered grids and then solved by the conjugate gradient Uzawa type method. The major advantages of the present method are the special simplicity, the ability in handling the Dirichlet boundary conditions, and no need of the pressure boundary condition. The method can also preserve the volume conservation and the discrete divergence free condition very well. The numerical results show that the proposed method is second order accurate and efficient.

Kernel Free Boundary Integral Method for 3D Stokes and Navier Equations on Irregular Domains

“…Since there are no discontinuous coefficients in the interface problem (18), numerical methods exist for solving it in the literature [20,34,39]. In this work, a finite difference method on staggered grid with a delicate correction technique will be taken into consideration, which can be seen as a promotion of [9] to 3D case.…”