Finite element level set formulations for modelling multiphase flows

Authors:
S. V. Shepel;S. Paolucci
Affiliations:
Laboratory for Thermohydraulics, Paul Scherrer Institut, Villigen PSI, CH-5232, Switzerland;Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN
Venue:
ICCMSE '03 Proceedings of the international conference on Computational methods in sciences and engineering
Year:
2003

Citing 4
Cited 1

A level set approach for computing solutions to incompressible two-phase flow

Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems

Journal of Computational Physics
An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow

SIAM Journal on Scientific Computing
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations

SIAM Journal on Scientific Computing

A hybrid variational front tracking-level set mesh generator for problems exhibiting large deformations and topological changes

Journal of Computational Physics

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Abstract

In this work, we present two Finite Element formulations of the Level Set method: the Streamline-Upwind/Petrov-Galerkin (SUPC) and the Runge-Kutta Discontinuous Galerkin (RKDC) schemes. Both schemes are constructed in such a way as to minimize the numerical diffusion inherently present in the discretized Level Set equations. In developing the schemes, special attention is given to the issues of mass-conservation and robustness. The RKDG Level Set formulation is original and represents the first attempt to apply the discontinuous Galerkin FE method to interface tracking. The performances of the two formulations are demonstrated on selected two-dimensional problems: the broken-dam benchmark problem and a mold-filling simulation. The problems are solved using unstructured triangulated meshes. We also provide comparison of our results with those obtained using the Volume-of-Fluid (VOF) method.