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Patch-Recovery Filters for Curvature in Discontinuous Galerkin-Based Level-Set Methods

Part of: Numerical approximation and computational geometry Two-phase and multiphase flows

Published online by Cambridge University Press:  01 February 2016

Florian Kummer  and
Tim Warburton
Florian Kummer*
Affiliation:
Department of Mechanical Engineering, Technische Universität Darmstadt, Otto-Berndt-Straße 2, 64287 Darmstadt, Germany
Tim Warburton
Affiliation:
Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005-1892, USA
*
*Corresponding author. Email addresses:kummer@fdy.tu-darmstadt.de (F. Kummer), timwar@rice.edu (T. Warburton)
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Abstract

In two-phase flow simulations, a difficult issue is usually the treatment of surface tension effects. These cause a pressure jump that is proportional to the curvature of the interface separating the two fluids. Since the evaluation of the curvature incorporates second derivatives, it is prone to numerical instabilities. Within this work, the interface is described by a level-set method based on a discontinuous Galerkin discretization. In order to stabilize the evaluation of the curvature, a patch-recovery operation is employed. There are numerous ways in which this filtering operation can be applied in the whole process of curvature computation. Therefore, an extensive numerical study is performed to identify optimal settings for the patch-recovery operations with respect to computational cost and accuracy.

Keywords

Discontinuous Galerkin (DG)multiphase flowscurvaturepatch recoveryfiltering

MSC classification

Secondary: 76T99: None of the above, but in this section 65Z05: Applications to physics 65D10: Smoothing, curve fitting
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 2 , February 2016 , pp. 329 - 353
Copyright
Copyright © Global-Science Press 2016 

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