摘要
针对非均匀介质中热蠕变流动问题,给出了有限单元方法与网格-粒子方法联合求解新技术,即有限单元方法求解欧拉网格节点上的未知量,分布于单元内部作为物质成分标记的粒子反映变形过程.有限元法求解动量方程和连续性方程时引入了速度场和压力场等阶插值的压力场稳定的Petrov-Galerkin方法,求解能量方程时采用了流线迎风Petrov-Galerkin方法,网格-粒子算法中采用双线性插值与有限单元插值函数对应.有限单元计算与网格-粒子计算相对独立,两种方法计算的数据通过有限单元节点传递.同时,实现了三角形单元的算法和程序,解决了复杂结构条件下不规则网格计算的问题.通过经典方腔热对流问题验证了程序,给出了不规则形态块体沉降算例,并分析了数值解的稳定性.
A hybrid method for modeling the creeping flow is proposed. In our method the so-called marker-incell （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 communicate through the nodal points. In addition, the triangular dement 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.
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2006年第4期1029-1036,共8页
Chinese Journal of Geophysics
基金
国家自然科学基金重点项目(40234043)资助
关键词
非均匀介质
热蠕变流动
网格-粒子
有限单元方法
Heterogeneous medium, Thermal creeping flow, Marker-in-cell, Finite element method
