swMATH ID: 
39197

Software Authors: 
Landet, Tormod; Mardal, KentAndre; Mortensen, Mikael

Description: 
Slope limiting the velocity field in a discontinuous Galerkin divergencefree twophase flow solver. Solving the NavierStokes equations when the density field contains a large and sharp discontinuity – such as a water/air free surface – is numerically challenging. Convective instabilities cause Gibbs oscillations which quickly destroy the solution. We investigate the use of slope limiters for the velocity field to overcome this problem in a way that does not compromise on the massconservation properties. The equations are discretised using a symmetric interiorpenalty discontinuous Galerkin finite element method that is divergencefree to machine precision. A slope limiter made specifically for exactly divergencefree (solenoidal) fields is presented and used to illustrate the difficulties in obtaining convectively stable fields that are also exactly solenoidal. The lessons learned from this are applied in constructing a simpler method based on the use of an existing scalar slope limiter applied to each velocity component. We show by numerical examples how both presented slope limiting methods are vastly superior to the naive nonlimited method. The methods can solve difficult twophase problems with high densityratios and high Reynolds numbers – typical for marine and offshore water/air simulations – in a way that conserves mass and stops unbounded energy growth caused by the Gibbs phenomenon. 
Homepage: 
https://arxiv.org/abs/1803.06976

Source Code: 
https://bitbucket.org/ocellarisproject/ocellaris/src/master/

Keywords: 
DG FEM;
divergencefree;
solenoidal;
NavierStokes;
twophase;
slope limiter;
Gibbs oscillations;
density jump

Related Software: 
SciPy;
SyFi;
FEniCS

Cited in: 
3 Documents
