报告地点：行健楼505
邀请人：陈金如教授
摘要：
Simulations of fluid and porous media couplings are important and challenging because of different governing equations and complicated interface conditions such as BJ and BJS relations. Most of numerical methods in the literature are based on finite element formulations in which the interface conditions are incorporated in the variational forms. One consequence is that the large errors across the interface due to low regularity of the solution if the mesh is not aligned with the interface. The large discrete system makes harder to use fast solvers.
In this talk, we propose a finite difference approach with unfitted meshes. For the coupling with a constant coefficient, by introducing several augmented variables along the interface, we can decouple the original problem as several Poisson/Helmholtz equations with intermediate jump conditions in the solution and the normal derivatives. One obvious advantage is that a fast Poisson/Helmholtz solver can be utilized. The augmented variables should be chosen such that the Beavers-Joseph-Saffman (BJS) and other interface conditions are satisfied.
When the viscosity is a variable or non-linear function, we cannot employ a fast solver. Thus, by introducing the minimum number of augmented variables, we can solve the pressure and velocity iteratively while avoiding solving a saddle point problem. The new method does not need the partial derivatives of the variable or non-linear viscosity. Non-trivial numerical examples confirm the efficiency of the proposed methods. Some interesting phenomena have been observed in the presented numerical simulations.
