An immersed interface method for the incompressible Navier-Stokes equations in irregular domains
D.V. Lea, B.C. Khooa,b, J. Perairea,c,*
aSingapore-MIT Alliance bMechanical Engineering Department, National University of Singapore, Kent Ridge Road, Singapore cDepartment of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA
ABSTRACT
We present an immersed interface method for the incompressible Navier-Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid. These forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of the singular forces is determined by solving a small system of equations at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second-order accurate projection method for pressure and velocity.
Keywords:
Immersed interface method; Navier-Stokes equations; Cartesian grid method; Finite difference; Fast Poisson solvers; irregular domains