An Approximation to Miscible Fluid Flows in Porous Media with Point Sources and Sinks by an Eulerian-Lagrangian Localized Adjoint Method and Mixed Finite Element Methods
An Approximation to Miscible Fluid Flows in Porous Media with Point Sources and Sinks by an Eulerian-Lagrangian Localized Adjoint Method and Mixed Finite Element Methods
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DOI：
10.1137/s1064827598349215
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发表时间：
2000-02
期刊：
影响因子：
--
通讯作者：
Hong Wang;D. Liang;R. Ewing;S. L. Lyons;Guan Qin
中科院分区：
文献类型：
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作者：
Hong Wang;D. Liang;R. Ewing;S. L. Lyons;Guan Qin
我们开发了一种欧拉-拉格朗日局部化伴随方法（ELLAM）-混合有限元方法（MFEM）的解决方案技术，精确的数值模拟耦合系统的偏微分方程（PDE），描述复杂的流体流动过程中的多孔介质。一个ELLAM，这是以前表现出优于许多广泛使用的方法在线性对流扩散偏微分方程的背景下，提出解决浓度的传输方程。由于精确的流体速度在数值模拟中是至关重要的，因此使用MFEM来求解压力方程的压力和达西速度。这最大限度地减少了标准方法中出现的数值困难，这些方法用于近似由压力微分然后乘以粗略系数引起的速度。的ELLAM-MFEM解决方案技术显着减少时间误差，对称化的控制输运方程，消除非物理振荡和/或过多的数值分散在许多模拟器，保存质量，并准确地处理边界条件。数值实验表明，ELLAM-MFEM方法在较粗的空间网格和较大的时间步长下，能够较准确地模拟多孔介质中不可压缩流体的混溶驱替问题，比许多方法的时间步长大一到两个数量级。此外，ELLAM-MFEM解决方案技术可以处理大的流度比，不连续的渗透率和孔隙度，张量形式的各向异性色散，和点源和汇。
We develop an Eulerian--Lagrangian localized adjoint method (ELLAM)-mixed finite element method (MFEM) solution technique for accurate numerical simulation of coupled systems of partial differential equations (PDEs), which describe complex fluid flow processes in porous media. An ELLAM, which was shown previously to outperform many widely used methods in the context of linear convection-diffusion PDEs, is presented to solve the transport equation for concentration. Since accurate fluid velocities are crucial in numerical simulations, an MFEM is used to solve the pressure equation for the pressure and Darcy velocity. This minimizes the numerical difficulties occurring in standard methods for approximating velocities caused by differentiation of the pressure and then multiplication by rough coefficients. The ELLAM-MFEM solution technique significantly reduces temporal errors, symmetrizes the governing transport equation, eliminates nonphysical oscillation and/or excessive numerical dispersion in many simulators, conserves mass, and treats boundary conditions accurately. Numerical experiments show that the ELLAM-MFEM solution technique simulates miscible displacements of incompressible fluid flows in porous media accurately with fairly coarse spatial grids and very large time steps, which are one or two orders of magnitude larger than the time steps used in many methods. Moreover, the ELLAM-MFEM solution technique can treat large mobility ratios, discontinuous permeabilities and porosities, anisotropic dispersion in tensor form, and point sources and sinks.