论文标题
用于图形拉普拉斯的多级光谱使储层模拟应用
Multilevel spectral coarsening for graph Laplacian problems with application to reservoir simulation
论文作者
论文摘要
我们将先前开发的两级粗化程序扩展为以混合鞍点形式写的图形拉普拉斯问题到完全递归的多层次情况。离散化的产生层次结构产生了高扫描模型的层次结构，因为它们在自然规范（在混合环境中）中提供了近似值。该属性使我们能够在三个应用程序中利用它们：（i）作为准确的减少模型，（ii）作为多级蒙特卡洛模拟（用于有限量离散量的应用中），以及（iii）在FAS中提供非线性操作员在FAS（完整近似方案）中提供非线性非线性压力方程式的序列。我们说明了在储层模拟中使用的许多流行的基准问题上，在所有三个应用程序中提出的多级技术的潜力。
We extend previously developed two-level coarsening procedures for graph Laplacian problems written in a mixed saddle point form to the fully recursive multilevel case. The resulting hierarchy of discretizations gives rise to a hierarchy of upscaled models, in the sense that they provide approximation in the natural norms (in the mixed setting). This property enables us to utilize them in three applications: (i) as an accurate reduced model, (ii) as a tool in multilevel Monte Carlo simulations (in application to finite volume discretizations), and (iii) for providing a sequence of nonlinear operators in FAS (full approximation scheme) for solving nonlinear pressure equations discretized by the conservative two-point flux approximation. We illustrate the potential of the proposed multilevel technique in all three applications on a number of popular benchmark problems used in reservoir simulation.
