Journal
ADVANCES IN WATER RESOURCES
Volume 171, Issue -, Pages -Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.advwatres.2022.104340
Keywords
Stokes flow; Porous media; Algebraic Multigrid Method; General purpose GPU; Krylov subspace solvers; Permeability; Permeability tensor
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This paper presents a high efficiency Stokes solver for incompressible flow in porous media. The solver utilizes a fast algebraic multigrid method on graphics processing units (GPUs) to reduce memory usage and accelerate computation. A simple MAC-type staggered finite difference discretization is used, and a coupled Stokes saddle-point type system is directly solved on a GPU. The method includes topological domain analysis on a GPU to remove isolated volumes with no flow. Various types of boundary conditions and efficient parallel strategies for GPUs are considered. The method is extensively benchmarked against analytical solutions and applied problems from digital rock physics. The results demonstrate the effectiveness and efficiency of the proposed method.
The paper is focused on high efficiency Stokes solver that is applied to the incompressible flow in porous media. Computational domains are represented by binarized 3D computed tomography voxel models. The solution procedure is constructed around a fast algebraic multigrid solver that utilizes the power of graphics processing units (GPUs). In order to minimize memory footprint and accelerate the solver, a simple MAC-type staggered finite difference discretization is used and a coupled Stokes saddle-point type system is solved directly on a GPU. The MAC discretization is discussed, taking particular care of internal solid boundaries around pores. The method includes topological domain analysis on a GPU, which removes isolated volumes with no flow in the domain (based on the connected component labeling), depending on the boundary conditions. We consider various types of boundary conditions and efficient parallel strategies for the GPUs, including fast matrix assembly and residual regularization. Our method is extensively benchmarked both against analytical solutions and applied problems from digital rock physics in terms of computational wall time, precision, approximation order, and convergence. We demonstrate that it takes up to 5-23 s on a modern GPU card to obtain a solution with 1.10-6 error residuals for 3D geometries with 300-4503 voxels and a porosity range of 5-37%.
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