TITLE:
A Kinematics Scalar Projection Method (KSP) for Incompressible Flows with Variable Density
AUTHORS:
Jean-Paul Caltagirone, Stéphane Vincent
KEYWORDS:
Projection Methods, Hodge-Helmholtz Decomposition, Navier-Stokes Equation, Incompressible Flows
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.5 No.2,
June
15,
2015
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.