A Discontinuous Galerkin Method for Viscous Compressible Multifluids

TL;DR

This paper introduces a generalized discontinuous Galerkin method tailored for multicomponent compressible fluid flows with pressure-dependent viscosity, employing high-order time discretization and analyzing energy consistency.

Contribution

It develops a novel DG scheme for viscous multifluids with pressure-dependent viscosity, including boundary condition handling and energy analysis.

Findings

The scheme achieves high accuracy in test cases.

Energy consistency is verified theoretically.

Applications demonstrate physical relevance.

Abstract

We present a generalized discontinuous Galerkin method for a multicomponent compressible barotropic Navier-Stokes system of equations. The system presented has a functional viscosity nu which depends on the pressure p=p(rho,mu_i) of the flow, with the density rho and the local concentration mu_i. High order Runge-Kutta time discretization techniques are employed, and different methods of dealing with arbitrary coupled boundary conditions are discussed. Analysis of the energy consistency of the scheme is performed in addition to inspection of the relative error of the solution compared to exact analytic test cases. Finally several examples, comparisons, generalizations and physical applications are presented.