AFiD-Darcy: A finite difference solver for numerical simulations of convective porous media flows

IF 7.2 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-03-13 DOI:10.1016/j.cpc.2025.109579

Marco De Paoli , Guru Sreevanshu Yerragolam , Detlef Lohse , Roberto Verzicco

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引用次数: 0

Abstract

We present an efficient solver for massively-parallel simulations of convective, wall-bounded and incompressible porous media flows. The algorithm consists of a second-order finite-difference pressure-correction scheme, allowing the use of an efficient FFT-based solver in problems with different boundary conditions. The parallelization method is implemented in a two-dimensional pencil-like domain decomposition, which enables efficient parallel large-scale simulations. The original version of the code presented by van der Poel et al. (2015) [35] has been modified to solve the Darcy equation for the momentum transport, representative of porous media flows driven by buoyancy. Two schemes are implemented to treat the diffusive term of the advection-diffusion equation, namely a fully implicit and semi-implicit formulation. Despite exhibiting a higher computational cost per time step, the fully implicit scheme allows an efficient simulation of transient flows, leading to a smaller time-to-solution compared to the semi-implicit scheme. The implementation was verified against different canonical flows, and the computational performance was examined. To show the code's capabilities, the maximal driving strength explored has been doubled as compared to state-of-art simulations, corresponding to an increase of the associated computational effort of about 8 to 16 times. Excellent strong scaling performance is demonstrated for both schemes developed and for domains with more than 10¹⁰ spatial degrees of freedom.

Program summary

Program Title: AFiD-Darcy

CPC Library link to program files: https://doi.org/10.17632/xhx3gzpj6n.1

Developer's repository link: https://github.com/depaolimarco/AFiD-Darcy

Licensing provisions: CC BY 4.0

Programming language: Fortran 90, MPI

External routines: FFTW3, HDF5

Nature of problem: Solving two- and three-dimensional Darcy equation coupled with a scalar field in a box bounded between two walls in one-direction and with periodic boundary conditions in the other two directions.

Solution method: Second order finite difference method for spatial discretization, third order Runge–Kutta scheme in combination with Crank–Nicolson for the implicit terms for time advancement, two dimensional pencil distributed MPI parallelization. Implicit and semi-implicit formulations for the solution of the diffusive terms in the scalar transport equation.

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对流多孔介质流动数值模拟的有限差分解算器

我们提出了一个有效的求解器，用于对流，有壁和不可压缩多孔介质流动的大规模并行模拟。该算法由二阶有限差分压力校正方案组成，允许在具有不同边界条件的问题中使用高效的基于fft的求解器。并行化方法是在二维铅笔状区域分解中实现的，可以实现高效的大规模并行模拟。van der Poel等人（2015）提出的原始版本的代码[35]已被修改，以解决动量输运的达西方程，代表由浮力驱动的多孔介质流动。采用两种格式处理平流扩散方程的扩散项，即全隐式和半隐式。尽管每个时间步长的计算成本较高，但与半隐式方案相比，完全隐式方案可以有效地模拟瞬态流动，从而缩短求解时间。针对不同的规范流对实现进行了验证，并对计算性能进行了检验。为了展示代码的能力，与最先进的模拟相比，所探索的最大驾驶强度增加了一倍，相应的计算工作量增加了约8到16倍。对于所开发的两种方案以及大于1010个空间自由度的域，都证明了出色的强缩放性能。程序摘要程序标题：AFiD-DarcyCPC库链接到程序文件：https://doi.org/10.17632/xhx3gzpj6n.1Developer's存储库链接：https://github.com/depaolimarco/AFiD-DarcyLicensing条款：CC BY 4.0编程语言：Fortran 90， mpi外部例程：FFTW3， hdf5问题的性质：解决二维和三维达西方程耦合标量场在一个方向上两个墙之间的盒子，在其他两个方向上具有周期性边界条件。求解方法：二阶空间离散化有限差分法，三阶Runge-Kutta格式结合Crank-Nicolson格式求解隐式时间推进项，二维铅笔分布MPI并行化。标量输运方程中扩散项的隐式和半隐式解。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.