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Abstract <p>We presented a numerical algorithm to solve Biot equations in a quasi-static state to upscale the anelastic properties of fractured-porous fluid-filled media. Biot equation couples elastic displacements and the relative fluid displacements in porous media. To solve the system of linear equations approximating the coupled model we suggest using the Krylov-type iterative method with field-split preconditioner. To construct the preconditioner we solve two independent decoupled problems of the smaller size. They are static elastic equations and equations governing relative fluid motion. Both sparse systems are solved with direct solvers. We focused on the applicability of the Elbrus processors to solve the discussed problem. We illustrate that Elbrus-based systems are capable of solving real-life simulations and dealing with large-scale problems. Moreover, Elbrus-based computations exhibited similar scalability under shared memory parallelization as those on Intel- and AMD-based architectures.</p>

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Numerical Solution of Biot Poroelastic Equations in Quasi-Static State Using Shared Memory Systems

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • S. A. Solovyev,
  • V. V. Lisitsa

摘要

Abstract

We presented a numerical algorithm to solve Biot equations in a quasi-static state to upscale the anelastic properties of fractured-porous fluid-filled media. Biot equation couples elastic displacements and the relative fluid displacements in porous media. To solve the system of linear equations approximating the coupled model we suggest using the Krylov-type iterative method with field-split preconditioner. To construct the preconditioner we solve two independent decoupled problems of the smaller size. They are static elastic equations and equations governing relative fluid motion. Both sparse systems are solved with direct solvers. We focused on the applicability of the Elbrus processors to solve the discussed problem. We illustrate that Elbrus-based systems are capable of solving real-life simulations and dealing with large-scale problems. Moreover, Elbrus-based computations exhibited similar scalability under shared memory parallelization as those on Intel- and AMD-based architectures.