Fractures should be simulated accurately given their significant effects on whole flow patterns in porous media. But such high-resolution simulation imposes severe computational challenges to numerical methods in the applications. Therefore, the demand for accurate and efficient technique is widely increasing. A near-linear complexity multiresolution decomposition is proposed for solving flow...
Containment of injected CO2 is of prime importance for long term integrity of CO2 geological storage projects. Structural/stratigraphic, dissolution, residual, capillary and mineral trapping mechanisms play significant roles on different time scales to keep the injected CO2 within the storage zone boundaries. In heterogeneous media the impact of capillary trapping mechanism becomes...
Fluid flow in porous media occurs on varied scales from pore to reservoir, where the fine scale heterogeneity may have a significant impact on large scale fluid flow. Resolving all pertinent scales in modeling and flow simulation is an arduous task limited by the availability of data and computational resources. Therefore, it is customary to use an upscaling procedure, in which the fine scale...
In this work, we develop and analyze an adaptive multiscale approach for Stokes problems in heterogeneous perforated domains. In many applications, these problems have a multiscale nature arising because of the perforations, their geometries, the sizes of the perforations, and configurations. Typical modeling approaches extract average properties in each coarse region, that encapsulate many...
