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

作者：Liao Jian Hui; Zhuang Zhuo^*

来源：Acta Mechanica Sinica, 2012, 28(5): 1309-1322.

DOI：10.1007/s10409-012-0103-x

• Two-phase flow
• XFEM
• SUPG/PSPG algorithm
• Consistency
• Discontinuous projection

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.

• 出版日期2012-10
• 单位清华大学