A Kinematics Scalar Projection Method (KSP) for Incompressible Flows with Variable Density

Jean-Paul Caltagirone¹, Stéphane Vincent²

¹UMR CNRS 5295, Département TREFLE, Institut de Mécanique et d’Ingénierie, Université de Bordeaux, Pessac Cedex, France.
²UMR CNRS 8208, Laboratoire Modélisation et Simulation Multi Echelle (MSME), Université Paris-Est, Marne-La-Vallée, France.

DOI: 10.4236/ojfd.2015.52019                

Abstract

A new scalar projection method presented for simulating incompressible flows with variable density is proposed. It reverses conventional projection algorithm by computing first the irrotational component of the velocity and then the pressure. The first phase of the projection is purely kinematics. The predicted velocity field is subjected to a discrete Hodge-Helmholtz decomposition. The second phase of upgrade of pressure from the density uses Stokes’ theorem to explicitly compute the pressure. If all or part of the boundary conditions is then fixed on the divergence free physical field, the system required to be solved for the scalar potential of velocity becomes a Poisson equation with constant coefficients fitted with Dirichlet conditions.

Keywords

Projection Methods, Hodge-Helmholtz Decomposition, Navier-Stokes Equation, Incompressible Flows

Conflicts of Interest

The authors declare no conflicts of interest.

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