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科学计算与偏微分方程数值解近展Recent Advances on Scientific Computing and Numerical PDEs小型研讨会

Kernel-free boundary integral method for two-phase Stokes equations with discontinuous viscosity on staggered grids 

Speaker

Haixia Dong , 湖南师范大学数学与统计学院

Time

12 Dec, 14:40 - 15:20

Abstract

A discontinuous viscosity coefficient makes the jump conditions of the velocity and normal stress −pn + μ∇u coupled together, which brings great challenges to some commonly used numerical methods to obtain accurate solutions. To overcome the difficulties, a kernel free boundary integral (KFBI) method combined with a modified marker-and-cell (MAC) scheme is developed to solve the two-phase Stokes problems with discontinuous viscosity. The main idea is to reformulate the two-phase Stokes problem into a single-fluid Stokes problem by using boundary integral equations and then evaluate the boundary integrals indirectly through a Cartesian grid-based method. Since the jump conditions of the single-fluid Stokes problems can be easily decoupled, the modified MAC scheme is adopted here and the existing fast solver can be applicable for the resulting linear saddle system. The computed numerical solutions are second order accuracy in discrete l2-norm for velocity and pressure as well as the gradient of velocity, and also second order accuracy in maximum norm for both velocity and its gradient, even in the case of high contrast viscosity coefficient, which is demonstrated in numerical tests.