Penalized Direct Forcing and Projection Schemes for Navier-Stokes

Abstract

This note presents a new method of direct forcing to deal with obstacles in incompressible flows. It mixes projection schemes and velocity L2 penalty schemes. The penalized direct forcing term is distributed in the velocity prediction and the correction equations. It leads to a natural treatment in the correction equation of the boundary conditions in pressure around obstacles. A numerical experiment provided an illustration of the method