We present a flexible scalable open-source computational framework, named SECUReFoam, based on the finite-volume library OpenFOAM(R), for flow and transport problems in highly heterogeneous geological media and other porous materials. The framework combines geostatistical pre- and post-processing tools with specialised Partial Differential Equations solvers. Random fields, for permeability and other physical properties, are generated by means of continuous or thresholded Gaussian random fields with various covariance/variogram functions. The generation process is based on an explicit spectral Fourier decomposition of the field which, although more computationally intensive than Fast Fourier Transform methods, allows a more flexible choice of statistical parameters and can be used for general geometries and grids. Flow and transport equations are solved for single-phase and variable density problems, with and without the Boussinesq approximation, and for a wide range of density, viscosity, and dispersion models, including dual-continuum (dual permeability or dual porosity) formulations. The mathematical models are here presented in details and the numerical strategies to deal with heterogeneities, equation coupling, and boundary conditions are discussed and benchmarked for the heterogeneous Henry and Horton-Rodgers-Lapwood problems, and other test cases. We show that our framework is capable of dealing with large permeability variances, viscous instabilities, and large-scale three-dimensional transport problems.
翻译:我们提出了一个灵活的开放源代码计算框架,称为SECUREFOAM(R),其依据是数量有限的库 OpenFOAM(R),用于高度多样化的地质媒体和其他多孔材料的流动和运输问题。框架将地理统计前和后处理工具与专门的局部差异方程式相结合。渗透性和其他物理属性的随机字段,由连续或封闭的高斯随机字段和各种常态/变异功能生成。生成过程基于一个清晰的光谱四氟化变异,尽管其计算强度大于快速四氟化变异方法,但允许更灵活地选择统计参数,并可用于一般的地理比例和网格。流动和运输方程式是单阶段和多密度问题的解决方案,使用或不使用布辛克近似,以及广泛的密度、粘度和分散模型,包括双连续性(多维度或双倍孔化)的配置。这里的数学模型以详细的细节和可变异性模型形式和可变式模型形式展示了亨利-更迭性模型,而我们则以可变式的模型和变式的模型则用于讨论。