Comparative Analysis of Methods for Solving Systems of Linear Algebraic Equations of a Special Form in the Hydraulic Fracture Propagation Modeling Problem
DOI:
https://doi.org/10.14529/cmse260203Keywords:
systems of linear algebraic equations, hydraulic fracturing, preconditioning, iterative methods, sparse matrices, parallel computing, academic tournamentAbstract
Methods for the numerical solution of systems of linear algebraic equations (SLAE) of a special form arising in the simulation of fluid flow in porous media and of hydraulic fracture propagation are considered. The methods discussed are used in the corporate software product line developed at PJSC Rosneft Oil Company. Particular attention is paid to parallel methods for solving sparse systems that are employed in corporate simulators. The mathematical formulation of the problem of the 2025 Rosneft Academic Tournament, related to the simulation of hydraulic fracturing, is presented. A distinctive feature of the problem is the coupled modeling of the elastic behavior of the rock and of fluid flow within the fracture, which requires the repeated solution of systems with a block matrix containing both sparse blocks and a dense block corresponding to the geomechanics equations. The presence of the dense block substantially distinguishes these systems from the classical sparse systems of reservoir simulation and calls for specialized algorithms. As part of the tournament, participants were asked to solve a sequence of 551 SLAEs of this special form. A comparative analysis of the finalist teams’ solutions is carried out in terms of the efficiency of the parallel methods used to solve the linear systems.
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