Time Stepping Along Characteristics with Incomplete Iteration for a Galerkin Approximation of Miscible Displacement in Porous Media
Time Stepping Along Characteristics with Incomplete Iteration for a Galerkin Approximation of Miscible Displacement in Porous Media
复制标题
DOI：
10.1137/0722059
复制
发表时间：
1985-10
影响因子：
2.9
通讯作者：
T. Russell
中科院分区：
文献类型：
--
作者：
T. Russell
用两个非线性耦合偏微分方程组来模拟多孔介质中一种不可压缩流体与另一种不可压缩流体的混溶驱替。压力方程是椭圆的，而浓度方程是抛物线的，但通常是对流占优的。一个顺序向后差分时间步进计划的定义，它近似的压力由一个标准的Galerkin程序和浓度的组合的Galerkin方法和方法的特征。最佳收敛速度在$L^2 $和$H^1 $证明了该计划和一个修改的版本，其中代数方程在每个时间步近似解决了有限数量的预处理共轭梯度迭代。时间步进沿着的浓度方程的双曲线部分的特性示出的结果比标准方法的时间截断误差更小。其他地方发表的数值结果已经证实，较大的时间步长是适当的。
Miscible displacement of one incompressible fluid by another in a porous medium is modeled by a nonlinear coupled system of two partial differential equations. The pressure equation is elliptic, while the concentration equation is parabolic but normally convection-dominated. A sequential backward-difference time-stepping scheme is defined; it approximates the pressure by a standard Galerkin procedure and the concentration by a combination of a Galerkin method and the method of characteristics. Optimal convergence rates in $L^2 $ and $H^1 $ are demonstrated for this scheme and for a modified version in which the algebraic equations at each time step are solved approximately by a limited number of preconditioned conjugate gradient iterations. Time stepping along the characteristics of the hyperbolic part of the concentration equation is shown to result in smaller time-truncation errors than those of standard methods. Numerical results published elsewhere have confirmed that larger time steps are appropriate...