A Kinematic Scalar Projection method (KSP) for incompressible flows with variable density

Jean-Paul Caltagirone (1) , Stéphane Vincent (1)

1 I2M - Institut de Mécanique et d'Ingénierie de Bordeaux

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 are 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.

Mots clés: Projection methods; Hodge-Helmholtz Decomposition; Navier-Stokes equation; Incompres-sible flows

Domaines: Mécanique des fluides [physics.class-ph]

Jean-Paul Caltagirone, Stéphane Vincent. A Kinematic Scalar Projection method (KSP) for incompressible flows with variable density. 2015. ⟨hal-01136868⟩