Patch-recovery filters for curvature in discontinuous Galerkin-based level-set methods
This work provides practical guidance for stabilizing curvature calculations in two-phase flow simulations, which is a known bottleneck for numerical stability in computational fluid dynamics.
The paper addresses numerical instabilities in curvature evaluation for two-phase flow simulations using a discontinuous Galerkin-based level-set method. It identifies optimal settings for patch-recovery filters that stabilize curvature computation, balancing computational cost and accuracy through extensive numerical tests.
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.