基于网格变动的油水驱动半正定问题迎风混合元方法

UPWIND-MIXED METHOD ON CHANGING MESHES FOR POSITIVE SEMI-DEFINITE PROBLEM OF TWO-PHASE MISCIBLE FLOW

在网格随时间变动的有限元空间上研究了不可压缩的两相渗流驱动问题.分别对饱和度方程扩散矩阵正定和半正定的情形,提出了基于网格变动的迎风混合元方法:混合元逼进压力方程,饱和度方程的对流项采用迎风格式来处理,扩散项则采用推广的混合元来逼进.在网格任意变动的情形下得到几乎最优的误差估计;对正定问题的格式进行改进,即在两个网格之间投影变化时采取近似解的线性构造,可以得到与固定网格时相同的最优收敛阶.

The upwind-mixed method is presented for the positive semi-definite and the positive definite problems of two phase miscible flow in porous media on dynamically changing meshes. It is shown that the obtained rate error estimates are almost optimal. After some modification of the scheme for the positive definite problem we can obtain the optimal rate error estimate that is well known for static meshes. Finally, the numerical experiments are given.