The presentation will focus on novel multilevel techniques applied to reservoir simulation equations. Specifically, an Element-based Algebraic Multigrid method (AMGe) is used to perform accurate numerical upscaling (coarsening). AMGe is a framework of multigrid methods for finite element discretizations. The components in AMGe are constructed from local element information, such as finite element matrices and element topology. This is in contrast to classical AMG, where only system coefficients are used to construct the hierarchy of coarse spaces. AMGe seeks to mitigate the shortcomings of algebraic multigrid and geometric multigrid by using both mesh information and system coefficients.
The traditional approach for upscaling resorts to computing effective properties of the subsurface (permeability/porosity) by homogenization (averaging) techniques. Our vision is to numerically upscale from the geological model and to recompute the coarse spaces used for upscaling when needed, i.e. when the physical properties of the system have changed. This ensures that our coarse simulation model is dynamically updated from the fine geological model and provides a flexible framework for simulating at different resolutions. Among other things, this can be utilized to enable large-scale uncertainty quantification and optimization where many (otherwise computationally expensive) realizations of the simulation model is needed.
The method will be demonstrated on challenging test cases by comparing the oil and water production of the original fine grid solution with that of the upscaled solutions.