Composable block solvers for the four-field double porosity/permeability model

JOURNAL OF COMPUTATIONAL PHYSICS

卷:386

Article

Joshaghani, M. S.¹  Chang, J.²  Nakshatrala, K. B.¹  Knepley, M. G.³ 

[1] Univ Houston, Dept Civil & Environm Engn, Houston, TX 77204 USA

[2] Rice Univ, Houston, TX 77251 USA

[3] SUNY Buffalo, Buffalo, NY USA

关键词: Iterative solvers;    Parallel computing;    Finite element discretizations;    H(div) elements;    Double porosity/permeability model;    Flow through porous media;   

DOI  :  10.1016/j.jcp.2019.02.020

来源: Elsevier

【 摘 要 】

The objective of this paper is twofold. First, we propose two composable block solver methodologies to solve the discrete systems that arise from finite element discretizations of the double porosity/permeability (DPP) model. The DPP model, which is a four-field mathematical model, describes the flow of a single-phase incompressible fluid in a porous medium with two distinct pore-networks and with a possibility of mass transfer between them. Using the composable solvers feature available in PETSc and the finite element libraries available under the Firedrake Project, we illustrate two different ways by which one can effectively precondition these large systems of equations. Second, we employ the recently developed performance model called the Time-Accuracy-Size (TAS) spectrum to demonstrate that the proposed composable block solvers are scalable in both the parallel and algorithmic sense. Moreover, we utilize this spectrum analysis to compare the performance of three different finite element discretizations (classical mixed formulation with H(div) elements, stabilized continuous Galerkin mixed formulation, and stabilized discontinuous Galerkin mixed formulation) for the DPP model. Our performance spectrum analysis demonstrates that the composable block solvers are fine choices for any of these three finite element discretizations. Sample computer codes are provided to illustrate how one can easily implement the proposed block solver methodologies through PETSc command line options. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free