用于大规模一氧化碳_2$$注入热模拟的受限压力-温度残差(CPTR)预处理器的性能

IF 2.1 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Matthias A. Cremon, Jacques Franc, François P. Hamon
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引用次数: 0

摘要

这项工作研究了一种新型预处理器的性能,这种预处理器是为热储层模拟案例设计的,最近在 Roy 等人(SIAM J. Sci. Comput. 42, 2020)和 Cremon 等人(J. Comput. Phys. 418C, 2020)的文章中介绍了它在大规模热 CO\(_2\) 注入案例中的性能。对于碳捕集与封存(CCS)项目而言,在超临界条件下注入 CO\(_2\) 通常比储层温度低几十度。热效应会对模拟结果产生重大影响,但也会给求解器带来许多挑战。更具体地说,众所周知,迭代线性求解器(如 GMRES)和基于约束压力残余(CPR)的物理分块预处理器的常规组合在热效应起重要作用时,会表现不佳或无法收敛。约束压力-温度残差(CPTR)预处理器保留了 CPR 的 \(2\times 2\) 块结构(椭圆/双曲),但在椭圆子系统中包含了温度。这样,求解器就能适当处理抛物能量方程的长程椭圆部分。椭圆子系统现在由两个方程组成,由 BoomerAMG(来自 HYPRE 库)的系统求解器处理。然后,全局平滑器 ILU(0) 被应用于整个系统,以处理局部双曲温度锋。我们在多物理场求解器 GEOS 中实施了 CPTR,并展示了各种大规模热 CCS 模拟案例的结果,包括笛卡尔网格和完全非结构网格,自由度高达数千万。CPTR 前处理程序大大减少了 GMRES 的迭代次数和运行时间,以前使用 CPR 时需要 24 小时,现在使用 CPTR 时只需几小时。我们在多个案例中使用数百个 CPU 内核得出了强大的扩展结果,并显示出接近线性的扩展。CPTR 对热佩克莱特数(比较平流和扩散效应)也几乎不敏感,适用于任何热环境。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Constrained pressure-temperature residual (CPTR) preconditioner performance for large-scale thermal CO $$_2$$ injection simulation

This work studies the performance of a novel preconditioner, designed for thermal reservoir simulation cases and recently introduced in Roy et al. (SIAM J. Sci. Comput. 42, 2020) and Cremon et al. (J. Comput. Phys. 418C, 2020), on large-scale thermal CO\(_2\) injection cases. For Carbon Capture and Sequestration (CCS) projects, injecting CO\(_2\) under supercritical conditions is typically tens of degrees colder than the reservoir temperature. Thermal effects can have a significant impact on the simulation results, but they also add many challenges for the solvers. More specifically, the usual combination of an iterative linear solver (such as GMRES) and the Constrained Pressure Residual (CPR) physics-based block-preconditioner is known to perform rather poorly or fail to converge when thermal effects play a significant role. The Constrained Pressure-Temperature Residual (CPTR) preconditioner retains the \(2\times 2\) block structure (elliptic/hyperbolic) of CPR but includes the temperature in the elliptic subsystem. Doing so allows the solver to appropriately handle the long-range, elliptic part of the parabolic energy equation. The elliptic subsystem is now formed by two equations, and is dealt with by the system-solver of BoomerAMG (from the HYPRE library). Then a global smoother, ILU(0), is applied to the full system to handle the local, hyperbolic temperature fronts. We implemented CPTR in the multi-physics solver GEOS and present results on various large-scale thermal CCS simulation cases, including both Cartesian and fully unstructured meshes, up to tens of millions of degrees of freedom. The CPTR preconditioner severely reduces the number of GMRES iterations and the runtime, with cases timing out in 24h with CPR now requiring a few hours with CPTR. We present strong scaling results using hundreds of CPU cores for multiple cases, and show close to linear scaling. CPTR is also virtually insensitive to the thermal Péclet number (which compares advection and diffusion effects) and is suitable to any thermal regime.

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来源期刊
Computational Geosciences
Computational Geosciences 地学-地球科学综合
CiteScore
6.10
自引率
4.00%
发文量
63
审稿时长
6-12 weeks
期刊介绍: Computational Geosciences publishes high quality papers on mathematical modeling, simulation, numerical analysis, and other computational aspects of the geosciences. In particular the journal is focused on advanced numerical methods for the simulation of subsurface flow and transport, and associated aspects such as discretization, gridding, upscaling, optimization, data assimilation, uncertainty assessment, and high performance parallel and grid computing. Papers treating similar topics but with applications to other fields in the geosciences, such as geomechanics, geophysics, oceanography, or meteorology, will also be considered. The journal provides a platform for interaction and multidisciplinary collaboration among diverse scientific groups, from both academia and industry, which share an interest in developing mathematical models and efficient algorithms for solving them, such as mathematicians, engineers, chemists, physicists, and geoscientists.
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