A fully conservative and shift-invariant formulation for Galerkin discretizations of incompressible variable density flow - Lundgren, Lukas; Nazarov, Murtazo (Journal of computational physics, 2024)
This paper introduces a formulation of the variable density incompressible Navier-Stokes equations by modifying the nonlinear terms in a consistent way. For Galerkin discretizations, the formulation leads to favorable discrete conservation properties without the divergence-free constraint being strongly enforced. In addition, the formulation is shown to make the density field invariant to global shifts. The effect of viscous regularizations on conservation properties is also investigated. Numerical tests validate the theory developed in this work. The new formulation shows superior performance compared to other formulations from the literature, both in terms of accuracy for smooth problems and in terms of robustness. •A new formulation for variable density incompressible flow is introduced.•The formulation leads to improved conservation properties without the divergence-free being strongly enforced.•The effect of viscous regularization on conservation properties is investigated.•Conservation of mass, kinetic energy, squared density, momentum and angular momentum are analyzed.•Mass is conserved by matching or reducing the polynomial degree of density to that of pressure.