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

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.