An Implicit High-Order Discontinuous Galerkin Approach for Variable Density Incompressible Flows
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In this work we present a high-order discontinuous Galerkin approach for the simulation of variable density incompressible (VDI) flows. Here, the density is treated as a purely advected property tracking possibly multiple (more than two) components, while the fluids interface is captured in a diffuse fashion by the high-degree polynomial solution thus not requiring any geometrical reconstruction. Specific care is devoted to deal with density over/undershoots, spurious oscillations at flows interfaces and Godunov numerical fluxes at inter-element boundaries. Time integration is performed with high-order implicit schemes thus preventing any time step restriction condition. Promising results with high-degree polynomial representation and relatively coarse meshes are achieved on numerical experiments involving high-density ratios (water–air) and the possible interaction of more than two components.
F. Massa is supported by the Supporting Talented Researchers (STaRS) programm of the University of Bergamo.
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