多孔介质可混溶流动问题的混合元与区域分裂特征差分格式

1 引 言 用区域分裂方法求微分方程的数值解,是近年来计算数学领域的—个新方法。这种方法通过分裂区域来减少所处理问题的规模,并实现并行计算,因此,特别适用于大范围的工程技术问题和数学物理问题。本文用这种方法处理平面可混溶不可压缩流动问题其中J=0.T].u为Darcy速度,p为压力,c为浓度,k为渗透率,μ（c)为流体粘性,c为注入井给定浓度,q为外界源汇项,q~+=max{q,0}.φ为孔隙度。D为扩散矩阵,本文D与u无关。即仅考虑分子扩散,边条件可取为第一或第二类边条件。本文考虑第一类初边值问题

DOMAIN DECOMPOSITION METHOD WITH CHARACTERISTIC FINITE DIFFERENCE PROCEDURE FOR MISCIBLE DISPLACEMENT IN POROUS MEDIA

Consider the numerical method for miscible displacement in porous media. We use the mixed finite element method to solve the pressure equation, use domain decomposition and characteristic finite difference to solve the concentration equation, so the concentration equation can he solved in subdomain parallelly. For this scheme we give the existence, uniqueness of the approximation solution and optimal L-error estimates.