Numerical method of modeling thermal creeping flow in heterogeneous medium

A hybrid method for modeling the creeping flow is proposed. In our method the so-called marker-in-cell (MIC) and the Finite Element Method (FEM) algorithm are combined together to simulate the thermal creeping flow concerning heterogeneous medium deformation. In particular, the unknown parameters at the Euler mesh-nodes are calculated using the FEM. The cell-markers in each element carry the material composition and history variables during the flowing process. The momentum and continuity equation are solved in terms of the pressure-stabilizing Petrov-Galerkin method (PSPG) with the equal-order interpolation of the velocity and pressure, and the energy equation is solved using the streamline upwind Petrov-Galerkin method (SUPG). In the MIC algorithm, the bilinear interpolation corresponds to the interpolation function in the finite elements. The FEM and MIC algorithm are independent of each other. The data in these two processes cornmunicate through the nodal points. In addition, the triangular element algorithm makes possible to solve the problems with irregular mesh-grid in complex structures. Our computation program has been verified with the classical Rayleigh-Benard convection problem. As an example, the descent of an irregular geometry block is calculated. The stability of numerical solution is also investigated.