Multiphase flow simulation for incompressible Navier–Stokes equations using constant coefficients for Poisson equation

The Projection Method is a well-known algorithm for solving Navier–Stokes equations which considers pressure effects only on the corrector time step, usually calculated with a Poisson equation and then added in the non-corrected velocity. In the present paper, we present an algorithm to numerically solve the Navier–Stokes equations for multiphase flows, with constant derivative coefficients of Poisson equation that is calculated only once each time step, even for Runge–Kutta schemes. It is called the Incremental Pressure-Correction Algorithm and works with a penalty method, instead of the Projection Method. Based on the verification and validation procedure, the present formulation was compared with the classic formulation based on the Projection Method and was also validated with experimental results. It was shown that the new pressure consideration can reduce computational effort without losing the time convergence order.