Incompressible navier-stokes solutions with a new primitive variable solver

Abstract

A new primitive variable RNS/NS formulation for incompressible viscous flow is presented. This formulation, which has been applied for both two- and three-dimensional flows, is a semi-implicit, time-marching method using standard primitive variables. For this scheme the discrete continuity equation is satisfied directly at each time step, without artificial compressibility or pressure Poisson concepts. All the linear terms (continuity, pressure gradients, diffusion) are treated implicitly and all the non-linear convection terms are treated explicitly. Since all acoustic behavior is implicit, a convection-only CFL stability condition results even for incompressible flow. This is true without a P t term added to the continuity equation. The formulation is robust and provides accurate solutions that compare well with experimental data.