标题： 用于多孔介质中多相流的代数多重网格预条件器 显示英文标题

标题： Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media

摘要： 多相流是在包括碳封存、污染物修复和地下水管理在内的广泛应用中的关键过程。 通常，该过程通过一个非线性偏微分方程组进行建模，该方程组是通过考虑每个相（例如，油、水）的质量守恒，并结合相速度与相压力关系的本构定律推导出来的。 在本研究中，我们开发并研究了用于求解由多相流模型的完全耦合和时间隐式处理得到的代数方程组的有效求解算法。 我们探讨了几种基于代数多重网格（AMG）的预条件器在求解线性化问题中的性能，包括直接应用于系统的“黑箱”AMG，一种新的约束压力残差多重网格（CPR-AMG）预条件器，以及一种通过雅可比矩阵的块分解产生的近似Schur补得到的新预条件器。 我们表明，新方法在由毛细管压力变化效应决定的问题特性方面最为稳健，并且表明块分解预条件器在计算效率和问题规模的最优扩展性方面都表现良好。 显示英文摘要

摘要： Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential equations derived by considering the mass conservation of each phase (e.g., oil, water), along with constitutive laws for the relationship of phase velocity to phase pressure. In this study, we develop and study efficient solution algorithms for solving the algebraic systems of equations derived from a fully coupled and time-implicit treatment of models of multiphase flow. We explore the performance of several preconditioners based on algebraic multigrid (AMG) for solving the linearized problem, including "black-box" AMG applied directly to the system, a new version of constrained pressure residual multigrid (CPR-AMG) preconditioning, and a new preconditioner derived using an approximate Schur complement arising from the block factorization of the Jacobian. We show that the new methods are the most robust with respect to problem character as determined by varying effects of capillary pressures, and we show that the block factorization preconditioner is both efficient and scales optimally with problem size.