A multiscale finite element method for coupled heat and water transfer in heterogeneous soils

Authors: LUO, CHENYI - Beijing University Of Chinese Medicine; SHI, YUANYUAN - Beijing University Of Chinese Medicine; Timlin, Dennis; EWING, ROBERT - The Climate Corporation; Fleisher, David; HORTON, ROBERT - Iowa State University; TULLY, KATHERINE - University Of Maryland; WANG, ZHUANGJI - University Of Maryland

Submitted to: Journal of Hydrology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 6/9/2022
Publication Date: 9/15/2022
Citation: Luo, C., Shi, Y., Timlin, D.J., Ewing, R., Fleisher, D.H., Horton, R., Tully, K., Wang, Z. 2022. A multiscale finite element method for coupled heat and water transfer in heterogeneous soils. Journal of Hydrology. 612:10828. https://doi.org/10.1016/j.jhydrol.2022.128028.
DOI: https://doi.org/10.1016/j.jhydrol.2022.128028

Interpretive Summary: Soil hydraulic and thermal properties vary spatially. In two-dimensional numerical modeling of soil processes, fully considering all the spatial variabilities requires fine computing grids (coordinates on which variables are computed) and may greatly increase the computing load. In this study, we developed a multi-scale finite element method (MsFEM) that can perform simulations on relatively coarse grids, but partially include spatial variabilities of soil properties. By performing the numerical simulation on coarse grids, the computing load can be decreased. By partially considering the spatial soil variabilities, the simulation results on the coarse gird can include some fine-scale spatial variations. Therefore, our proposed numerical scheme can leverage the accuracy and the computing efficiency on soil hydraulic and thermal simulations. This research will be useful to researchers, consultants and practitioners who carry out simulations of soil processes.

Technical Abstract: Large-scale modeling of coupled heat and water dynamics is challenging due to the spatial variabilities of soil hydraulic and thermal properties. A multi-scale finite element method (MsFEM) has been designed for simulating liquid water fluxes in unsaturated soils. In this study, the MsFEM approach is expanded as a new scheme that can handle coupled soil heat and water transfer. Two groups of MsFEM base functions are constructed to incorporate the heterogeneities in soil hydraulic conductivity and thermal conductivity, and a Petrov-Galerkin formulation is adopted to implement the proposed MsFEM scheme. The MsFEM scheme is also exploited as a sequential solver when soil heat and water transfer are expressed in a partially coupled formulation (Wang et al., 2022). Numerical examples illustrate that, without essentially increasing the computing load, the MsFEM scheme can improve the accuracy up to 50% compared to the plain finite element method (FEM), for the thermally driven water (including vapor) transfer. Some small-scale spatial variations in soil temperature can only be revealed with the MsFEM scheme. If the MsFEM sequential solver is applied, the coupled heat and water transfer model with MsFEM schemes can be rewritten into a sequence of modules, where liquid water transfer, heat transfer and vapor transfer are modeled step-by-step. With the MsFEM sequential solver, a flexible modeling architecture can be achieved at the cost of a relatively small increase of error (<5%). Therefore, the MsFEM scheme presented in this study is an effective numerical approach to simulating coupled heat and water transfer in heterogeneous soils.