多孔介质中两相不可压缩可混溶驱动问题的动态混合元方法及其特征修正格式

THE DYNAMIC MIXED FINITE ELEMENT METHODS FOR INCOMPRESSIBLE MISCIBLE DISPLACEMENT IN POROUS MEDIA

许多依赖时间的问题涉及到局部化现象,如突出的前沿位置、激波、边界层等, 其位置随时间而变动.多孔介质中两相不可压缩可混溶驱动问题是一典型的、有代表性 的"局部化现象"问题,其数学模型为耦合非线性偏微分方程组的初边值问题.为减轻数 值解在局部前沿位置的数值振荡,提高解的精确性,本文给出了该问题的动态混合元格 式和沿特征线修正的动态混合元格式,证明了其收敛性,并给出了误差估计.

Many time-dependent problems involve localized phenomena, such as sharp fronts, shocks, and layers, which move with time. Miscible displacement problem in porous media is a typical, representative problem with localized phenomena, the models of which can be described as a coupled system of non-linear partial differential equations. To capture this moving local phenomena improve the numerical solution's precision, we present a dynamic mixed finite element we that with its modified form along the characteristic orve for incompressible miscible displacement in porous media, and discuss their convergence and error estimates.