Efficient Solvers for Numerical Simulation of Methane Hydrate

doi:10.11871/jfdc.issn.2096-742X.2026.05.008

Abstract

Abstract:

[Objective] The selection and optimization of sparse linear solvers are of significant importance in fully implicit numerical simulations. [Methods] The computational performance and applicability of two direct solvers (LAPACK and MUMPS) and two iterative solvers (rocALUTION and HYPRE) were evaluated and compared across different grid scales to analyze the influence of solver selection, with the numerical results validated against experimental data. [Results] Solver selection shows a decisive influence on computational speed for the implicit solution of nonlinear equations. For small to medium-scale problems with grid numbers ranging from thousands to hundreds of thousands, the MUMPS-based direct solver outperforms the iterative solver HYPRE. For large-scale problems with one million or more grid cells, the iterative solver HYPRE demonstrates higher efficiency and better scalability. [Conclusions] For implicit solutions of nonlinear equations on grid scales up to tens of thousands of cells, the MUMPS-based direct solver outperforms iterative solvers. For million-grid-scale simulations, parallel direct solvers or preconditioned iterative methods are required. This study provides a quantitative basis for selecting and optimizing sparse linear solvers in implicit numerical simulations.

Key words: sparse linear systems, FISH simulator, solver, MUMPS, HYPRE

LYU Qiunan, XU Ran, LIN Ancheng, WANG Wu, LI Gang, LI Xiaosen. Efficient Solvers for Numerical Simulation of Methane Hydrate[J]. Frontiers of Data and Computing, 2026, 8(5): 96-107, https://cstr.cn/32002.14.jfdc.CN10-1649/TP.2026.05.008.

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References 18

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参数	数值
反应器有效容积（L）	88.3
气体组分（-）	99.9% CH₄
石英砂孔隙度（%）	52.17
注入气体总量（mol）	181.4
注水量（kg）	30.97
生成结束最终温度（℃）	11.7
初始气体饱和度S_G（%）	27.80
初始水饱和度S_A（%）	44.94
初始水合物饱和度S_H（%）	27.26

操作系统	Linux x86-64 Centos 7
编译器	compiler/intel/2017.5.239
MPI	mpi/hpcx/2.7.4/intel-2017.5.239
计算节点异构加速卡	海光一号CPU（32核心）+128 G内存 4×DCU（Z100，16 GB显存）
LAPACK	Intel MKL
MUMPS	MUMPS_5.4.1+Metis-4.0.3
rocALUTION	rocm/rocm-3.9.1/rocalution
HYPRE	hypre-v2.32+Intel MKL

模拟算例	总耗时（s）	构建矩阵占比（%）	求解方程组占比（%）
RUN 1-725	22,130	33.39	41.65
RUN 2-725	1,272	14.80	83.29
RUN 3-725	33,648	11.39	88.26
RUN 4-725	11,910	2.97	96.31

模拟算例	总耗时（s）	构建矩阵占比（%）	求解方程组占比（%）
RUN 2-725	1，272	14.80	83.29
RUN 2-1，450	4，472	13.61	85.19
RUN 2-2，900	10，371	14.68	84.34
RUN 2-11，600	104，276	13.29	86.02