Title: Comparison of a least-square weighted residual method and the Taylor–Galerkin method based on level set formulation for interface capturing

Authors: Hyoung Gwon Choi

Addresses: Department of Mechanical Engineering, Seoul National University of Science and Technology, 172 Gongreung-2 Dong, Nowon-Gu, Seoul, 139-743, Korea

Abstract: In this study, a least-square weighted residual method and the Taylor–Galerkin method have been adopted for the discretisation of the two hyperbolic-type equations of level set method: advection and reinitialisation equations. The accuracy and efficiency of the two methods were compared by solving a time-reversed vortex flow and a three-dimensional broken dam flows. A four-step splitting P1P1 finite element method was used for the solution of the incompressible Navier–Stokes equations. These numerical experiments showed that both the least-square weighted residual method and the Taylor–Galerkin method were first-order accurate in space and that the least-square method was more accurate and conservative than Taylor–Galerkin method in terms of mass error.

Keywords: least-squares weighted residual method; Taylor–Galerkin method; level set method; advection; reinitialisation; time-reversed vortex flow; 3D broken dam flows; finite element method; FEM; incompressible Navier–Stokes equations; direct numerical simulation; DNS; free surface flow.

DOI: 10.1504/PCFD.2011.041016

Progress in Computational Fluid Dynamics, An International Journal, 2011 Vol.11 No.3/4, pp.169 - 174

Published online: 28 Jun 2011 *

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