AI Chat Paper
Discover the SciOpen Platform and Achieve Your Research Goals with Ease.
Search articles, authors, keywords, DOl and etc.
{{expandStatus?'Exit ':''}}Advanced Search
(
The Richards equation has been widely used to describe unsaturated flow in porous media, but its thermodynamical consistency has been scarcely investigated. In this paper, a thermodynamically consistent formulation of Richards equation is established on the basis of the free energy concept and the second law of thermodynamics. The capillary effect is described by an interfacial free energy and its corresponding chemical potential. The formulation takes the water saturation as the primary variable as well as chemical potential gradient as the primary driving force. An appealing feature is that the formulation follows an energy dissipation law, which implies the consistency to the second law of thermodynamics. Furthermore, a linearized and energy stable time discretized method is proposed for the model. Numerical results confirms the thermodynamical consistency of the formulation.
Cai, J., Jin, T., Kou, J., et al. Lucas-Washburn equation-based modeling of capillary-driven flow in porous systems. Langmuir, 2021, 37(5): 1623-1636.
DiCarlo, D. A. Stability of gravity-driven multiphase flow in porous media: 40 years of advancements. Water Resources Research, 2013, 49: 4531-4544.
Farthing, M. W., Ogden, F. L. Numerical solution of richards’ equation: A review of advances and challenges. Soil Science Society of America Journal, 2017, 81: 1257-1269.
Feng, X., Qiao, Z., Sun, S., et al. An energy-stable Smoothed Particle Hydrodynamics discretization of the Navier-Stokes-Cahn-Hilliard model for incompressible two-phase flows. Journal of Computational Physics, 2023, 479: 111997.
Kou, J., Sun, S. Thermodynamically consistent modeling and simulation of multi-component two-phase flow with partial miscibility. Computer Methods in Applied Mechanics and Engineering, 2018, 331: 623-649.
Kou, J., Chen, H., Du, S., et al. An efficient and physically consistent numerical method for the Maxwell-Stefan-Darcy model of two-phase flow in porous media. International Journal for Numerical Methods in Engineering, 2023a, 124(3): 546-569.
Kou, J., Wang, X., Chen, H., et al. An energy stable, conservative and bounds-preserving numerical method for thermodynamically consistent modeling of incompressible two-phase flow in porous media with rock compressibility. International Journal for Numerical Methods in Engineering, 2023b, 124(11): 2589-2617.
Kou, J., Wang, X., Du, S., et al. An energy stable linear numerical method for thermodynamically consistent modeling of two-phase incompressible flow in porous media. Journal of Computational Physics, 2022, 451: 110854.
Qiao, Z., Sun, S. Two-phase fluid simulation using a diffuse interface model with Peng-Robinson equation of state. SIAM Journal on Scientific Computing, 2014, 36: B708-B728.
Richards, L. A. Capillary conduction of liquid through porous media. Physics, 1931, 1: 318-333.
Stokke, J. S., Mitra, K., Storvik, E., et al. An adaptive solution strategy for Richards’ equation. Computers & Mathematics with Applications, 2023, 152: 155-167.
Vodák, R., Fürst, T., et al. The difference between semi-continuum model and Richards’ equation for unsaturated porous media flow. Scientific Reports, 2022, 12(1): 7650.
Wang, X., Kou, J., Cai, J. Stabilized energy factorization approach for Allen-Cahn equation with logarithmic Flory-Huggins potential. Journal of Scientific Computing, 2020, 82: 25.
Xiong, Y. Flow of water in porous media with saturation overshoot: A review. Journal of Hydrology, 2014, 510: 353-362.
Zha, Y., Yang, J., Shi, L., et al. Simulating one-dimensional unsaturated flow in heterogeneous soils with water content-based richards equation. Vadose Zone Journal, 2013, 12(2): 1-13.
Zha, Y., Yang, J., Zeng, J., et al. Review of numerical solution of Richardson-Richards equation for variably saturated flow in soils. WIREs Water, 2019, 6(5): e1364.
This article is distributed under the terms and conditions of the Creative Commons Attribution (CC BY-NC-ND) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
京公网安备11010802044758号