半正定两相驱动问题的多步有限体积方法及其理论分析

考虑多维半正定两相驱动方程的初边值问题,在非结构网格上构造多步的迎风有限体积格式,利用微分方程先验估计理论证明了格式的离散模形式的误差估计为D(△t~2 h),其中△t和h分别表示时空步长．数值算例进一步验证了格式的有效性．

Analysis of Multistep Finite Volume Methods for Positive Semidefinite Problem of Two-Phase Incompressible Flow

The multidimensional positive semidefinite problem of two-phase incompressible flow in porous media with initial-boundary conditions is considered here. The equations are discretized by multistep upwind finite volume methods on unstructured meshes. It is proved that the error estimates in discrete norms are of order $O(\Delta t^2+h)$, where $\Delta t$ denotes the time step and $h$ denotes the space step. Numerical examples are given at the end to show the efficiency of the method.