Volume 19, Issue 2
Patch-Recovery Filters for Curvature in Discontinuous Galerkin-Based Level-Set Methods

Florian Kummer & Tim Warburton

Commun. Comput. Phys., 19 (2016), pp. 329-353.

Published online: 2018-04

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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.

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@Article{CiCP-19-329, author = {}, title = {Patch-Recovery Filters for Curvature in Discontinuous Galerkin-Based Level-Set Methods}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {2}, pages = {329--353}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.191114.140715a}, url = {http://global-sci.org/intro/article_detail/cicp/11091.html} }
TY - JOUR T1 - Patch-Recovery Filters for Curvature in Discontinuous Galerkin-Based Level-Set Methods JO - Communications in Computational Physics VL - 2 SP - 329 EP - 353 PY - 2018 DA - 2018/04 SN - 19 DO - http://dor.org/10.4208/cicp.191114.140715a UR - https://global-sci.org/intro/article_detail/cicp/11091.html KW - AB -

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.

Florian Kummer & Tim Warburton. (2020). Patch-Recovery Filters for Curvature in Discontinuous Galerkin-Based Level-Set Methods. Communications in Computational Physics. 19 (2). 329-353. doi:10.4208/cicp.191114.140715a
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