A consistent projection-based SUPG/PSPG XFEM for incompressible two-phase flows

作     者：Jian-Hui Liao Zhuo Zhuang 

作者机构：School of AerospaceTsinghua University 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2012年第28卷第5期

页      面：1309-1322页

核心收录：

学科分类：080704[工学-流体机械及工程] 08[工学] 080203[工学-机械设计及理论] 0807[工学-动力工程及工程热物理] 0802[工学-机械工程] 

主　　题：Two-phase flow XFEM SUPG/PSPG algorithm Consistency Discontinuous projection 

摘      要：In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin （SUPG/PSPG） extended finite element method （XFEM） is presented to model incompressible immiscible two-phase flows. As the application of linear elements in SUPG/PSPG schemes gives rise to inconsistency in stabilization terms due to the inability to regenerate the diffusive term from viscous stresses, the numerical accuracy would deteriorate dramatically. To address this issue, projections of convection and pressure gradient terms are constructed and incorporated into the stabilization formulation in our method. This would substantially recover the consistency and free the practitioner from burdensome computations of most items in the residual. Moreover, the XFEM is employed to consider in a convenient way the fluid properties that have interfacial jumps leading to discontinuities in the velocity and pressure fields as well as the projections. A number of numerical examples are analyzed to demonstrate the complete recovery of consistency, the reproduction of interfacial discontinuities and the ability of the proposed projection-based SUPG/PSPG XFEM to model two-phase flows with open and closed interfaces.