一种解耦方案用于求解基质酸化中改进Darcy-Brinkman-Forchheimer框架的质量与动量守恒方程
A Decoupled Scheme to Solve the Mass and Momentum Conservation Equations of the Improved Darcy-Brinkman-Forchheimer Framework in Matrix Acidization
AI总结：
针对基质酸化模拟中改进DBF框架的压力-速度耦合线性系统难以高效求解的问题，本文提出一种解耦方案，将其拆分为可并行迭代求解的压力和速度两个独立线性系统，并通过数值实验验证了方案的正确性与更高计算效率。
摘要：
由于过程中孔隙度不断变化，基质酸化模拟是多孔介质流动研究中的一项具有挑战性的任务。改进的DBF框架是进行此类模拟的一种模型，其数值格式将质量守恒方程和动量守恒方程一起离散，形成一个压力-速度线性系统。然而，由于系数矩阵的对角线上出现零元素，该线性系统只能通过直接求解器同时求解压力和速度。考虑到基质酸化模拟的大规模特性，直接求解器的求解时间并非不可容忍。因此，本文提出一种解耦方案，将耦合的压力-速度线性系统解耦为两个独立的线性系统：一个用于求解压力，另一个用于求解速度。这两个新的线性系统都可以通过并行迭代求解器求解，从而保证大规模模拟能够在合理的时间周期内完成。通过数值实验验证了该解耦方案的正确性及其更高的计算效率。
英文摘要：
Matrix acidization simulation is a challenging task in the study of flows in porous media, due to the changing porosity in the procedure. The improved DBF framework is one model to do this simulation, and its numerical scheme discretises the mass and momentum conservation equations together to form a pressure-velocity linear system. However, this linear system can only be solved by direct solvers to solve for pressure and velocity simultaneously, since zeros appear in the diagonal of the coefficient matrix. Considering the large-scale attribute of matrix acidization simulation, the solving time of direct solvers is not intolerant. Thus, a decoupled scheme is proposed in this work to decouple the coupled pressure-velocity linear system into two independent linear systems: one is to solve for pressure, and the other one is to solve for velocity. Both of the new linear systems can be solved by parallel and iterative solvers, which guarantees the large-scale simulation can be finished in a reasonable time period. A numerical experiment is carried out to demonstrate the correctness of the decoupled scheme and its higher computing efficiency.
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