Efficient multiscale preconditioners for large-scale highly heterogeneous flow.

MATH SEMINAR

 Speaker: Shubin Fu

Dr. Shubin Fu is an Assistant Professor at Eastern Institute of Technology, Ningbo. He has published more than 20 papers in journals such as SIAM Multiscale Modeling & Simulation, CMAME, JCP, etc. Research Field: Multiscale Model Reduction with applications in Physics, Geophysics, Computational Mechanics / Electromagnetics, Hydrology & Petroleum Engineering, Scientific Computing, Deep Learning.   

Title: Efficient multiscale preconditioners for large-scale highly heterogeneous flow

Abstract: We propose efficient and robust preconditioners for large-scale incompressible flow in highly heterogeneous porous media. We start from the discretization of the first-order form for the single phase incompressible flow and apply a velocity elimination strategy to obtain an equation with pressure as the only unknown. Then an efficient two- grid preconditioner is designed to solve this equation. The key component of the preconditioner is adoption of a non-standard coarse space that contains the media's heterogeneity information. We solve a carefully constructed spectral problem in each coarse element to form the non-standard coarse space. Rich numerical tests with several types of large-scale three-dimensional highly heterogeneous permeability fields are presented. The experimental results show that our generalized multiscale space based preconditioner is robust with respect to the contrast, size and geometry of the permeability felds. We also successfully apply this preconditioner for multiphase flow simulation and transport problems arising from reservoir simulation. We will also introduce how to extend this two-grid preconditioner to mutigrid regime.