Unstructured Adaptive Mesh Refinement for Flow in Heterogeneous Porous Media
Mohammad Karimi-Fard, Louis J. Durlofsky · Proceedings · 2014
Summary The spatial resolution required in a simulation model depends on the type and degree of geological heterogeneity, along with the flow physics and well locations. The use of adaptive mesh refinement (AMR) enables the grid to adapt dynamically during the course of the simulation, which facilitates the efficient use of computational resources. In this work we present a finite-volume-based AMR procedure that is suitable for complex reservoir models such as those characterized by fractures or channels. The approach uses a fully unstructured hierarchical grid to accurately represent complex geological features. An important aspect of the method is the use of flow-based global transmissibility upscaling, which provides accurate cell-to-cell transmissibilities at any level of coarsening. The performance of the method is illustrated for problems involving two-dimensional channelized and fractured systems. High levels of solution accuracy relative to reference fine-scale results are observed for both cases, and the AMR models are shown to consistently use less than 30% of the cells in the underlying fine-grid representation. For fractured systems, the method essentially provides a dual-continuum coarse-scale representation, and can thus be viewed as a dual-continuum-AMR technique.