Coupled heat and water transfer in heterogeneous and deformable soils: Numerical model using mixed finite element method

Authors: WANG, ZHUANGJI - University Of Maryland; Timlin, Dennis; LIU, GANG - China Agricultural University; Fleisher, David; SUN, WENGUANG - University Of Nebraska; BEEGUM, SAHILA - University Of Nebraska; HEITMAN, JOSHUA - North Carolina State University; REN, TUSHENG - China Agricultural University; CHEN, YAN - China Agricultural University; Reddy, Vangimalla

Submitted to: Journal of Hydrology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 2/26/2024
Publication Date: 3/18/2024
Citation: Wang, Z., Timlin, D.J., Liu, G., Fleisher, D.H., Sun, W., Beegum, S., Heitman, J., Ren, T., Chen, Y., Reddy, V. 2024. Coupled heat and water transfer in heterogeneous and deformable soils: Numerical model using mixed finite element method. Journal of Hydrology. 634. Article e131068. https://doi.org/10.1016/j.jhydrol.2024.131068.
DOI: https://doi.org/10.1016/j.jhydrol.2024.131068

Interpretive Summary: A soil profile is not perfectly uniform and can be compacted or expanded under natural conditions and agricultural management. To achieve an optimal performance in two dimensional simulations of soil physical processes, model designs should include the spatial heterogeneity and deformation in soils. In this study, we developed a mixed finite element scheme to perform heat and water transfer simulations in soils, with the abilities to handle the non-uniformity and non-rigidity states of soils. By adaptively increasing or decreasing the model resolution based on the degree of spatial heterogeneity, the model can leverage the spatial resolution of the simulation results and the computing time. By adding the deformation as a separate subroutine, soil deformation can be simulated when external load exists, and the deformation information can be transferred to soil heat and water subroutines. This research will be useful to researchers, consultants and practitioners who carry out simulations of soil physical processes.

Technical Abstract: We present a generic model framework to perform coupled heat and water transfer (CHWT) simulations in heterogeneous and non-rigid soils. Heterogeneities include instantaneous variations in soil hydraulic and thermal properties due to transient water content and temperature distributions. A mixed finite element method (FEM) is proposed as the numerical solver for the fully coupled version of the Philip and de Vries (1957) CHWT model, which can achieve both local and global conservation of mass and energy. Based on the mixed FEM scheme, a gradient measure and a clustering model (k-means) are used to trace the regions with large instantaneous heterogeneities, and an adaptive mesh refinement technique is included to improve the spatial resolution and simulation accuracy in the heterogeneous regions. A quasi-static soil (mesh) deformation model is developed as a separate module and prefixed to the mixed FEM scheme. When external load is applied, soil deformation is simulated with an updated Lagrange formulation, and the local water content and temperature changes due to soil compaction or expansion are updated in the CHWT model. Illustrative examples, including thermally induced soil water transfer and water infiltration with and without external loads, demonstrate the ability of the model framework to provide plausible CHWT results, especially the refined solutions near the wetting fronts and the water content and temperature distributions when the soil is non-rigid. The method for incorporating soil spatial heterogeneity and non-rigidity in CHWT simulations can be applied to existing soil simulators, e.g., HYDRUS or 2DSOIL.