基于有限体积法的冻土水热耦合程序开发及验证

土体冻结和融化时的水分迁移、相变与传热是一个相互影响的耦合过程。采用基于有限体积法的开源软件OpenFOAM，编制描述土体冻融过程的水热耦合计算程序。首先，基于土体水分和热量迁移基本方程、水分相变与温度的平衡方程，同时考虑相变对水分特征参数和热特性参数的影响以及相变潜热对传热过程的影响，建立冻土水热耦合数学模型。然后，采用基于多面体网格的有限体积方法对水热耦合控制方程进行空间离散，采用全隐式向后差分方法对方程进行时间离散，由此编制冻土水热耦合计算程序。该程序具有良好的几何适应性、质量和能量守恒性，具备面向复杂问题的并行计算功能。最后，采用该程序对两组不同温度边界条件的室内土体冻结试验进行数值模拟，并与试验结果进行对比，结果表明该程序可以较为准确地模拟土体冻结过程中温度场和水分场的演化特征。

Code development and verification for coupled process of water migration and heat transfer of frozen soil based on finite volume method

During soil freezing and thawing, water migration, phase transition and heat transfer are a multi-field coupled process in which these factors affect each other. In this study, a mathematical model for the coupling process of water migration and heat transfer was constructed by solving a simultaneous equation group, which contains the basic equations of water migration and heat transfer, and the equilibrium equation of water phase change and temperature. In the mathematical model, the effects of water phase change on hydraulic and thermal parameters were considered, so was the effect of latent heat in water phase change. Also, a code for the coupled heat transfer and water migration simulation was developed based on the finite volume method for the spatial discretization and fully implicit backward difference scheme for the time discretization. The code supporting unstructured mesh can ensure the conservation of mass and energy. It also has a parallel function, which can be used for the calculation of complex problems. Furthermore, an indoor soil freezing tests with two different temperature boundary conditions were conducted, and the corresponding numerical calculations were subsequently conducted. The experimental results generally matched the calculated ones, so the developed numerical simulation program can well simulate the evolution characteristics of the temperature field and water field during the soil freezing process. Hence, the established OpenFOAM program is an effective method to simulate the coupling process of water migration and heat transfer for the frozen soil.