Efficient projection kernels for discontinuous Galerkin simulations of disperse multiphase flows on arbitrary curved elements

Hybridizable discontinuous Galerkin method for curved domains

In this work we present a technique to numerically solve partial differential equations (PDE’s) defined in general domains Ω. It basically consists in approximating the domain Ω by polyhedral subdomains Dh and suitably defining extensions of the solution from Dh to Ω. More precisely, we solve the PDE in Dh by using a numerical method for polyhedral domains. In order to do that, the boundary con...

A Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Arbitrary Grids

A reconstruction-based discontinuous Galerkin method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. In this method, an in-cell reconstruction is used to obtain a higher-order polynomial representation of the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstruction is used to obtain a continuous polynomial solution on t...

High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics

A projection approach for multiphase flows

An Eulerian projection approach for incompressible variable-density two-phase flows is presented. The Navier-Stokes equations governing these flows are reformulated to take the form of the corresponding equations for the lighter phase with a constant density, which can be efficiently solved using standard numerical methods. The effect of the additional mass in the heavier phase is accounted for...

A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows

The accurate conservative level set (ACLS) method of Desjardins et al. [O. Desjardins, V. Moureau, H. Pitsch, An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J. Comput. Phys. 227 (18) (2008) 8395–8416] is extended by using a discontinuous Galerkin (DG) discretization. DG allows for the scheme to have an arbitrarily high order of accuracy with the smal...