(219d) A Data-Driven Numerical Framework for the Richards Equation for Sustainable Irrigation and Food Production
AIChE Annual Meeting
2023
2023 AIChE Annual Meeting
Environmental Division
Fundamentals of Environmental Kinetics and Food, Energy, and Water Systems
Tuesday, November 7, 2023 - 1:24pm to 1:42pm
To further incorporate the underlying physics of water flow dynamics and conservation in soil, in the second part of this talk, we introduce the first data-driven global random walk algorithm to solve the FVM-based adaptive L-scheme. A key assumption made in existing global random walk algorithms for solving the Richards equation is that the pressure head is proportional to the number of particles in a discretized cell [4]. Nevertheless, we have shown that this assumption is invalid, and the relationship between the pressure head and the number of particles may not be continuous, smooth, or explicit. Instead, we propose a novel data-driven approach and used two neural networks to accurately learn the mapping and inverse mapping between the pressure head and the number of particles. Coupling this with the adaptive L-scheme, we show that our data-driven framework not only is the first-of-its-kind that can solve 3-D Richards equation, but also outperformed commercial and state-of-the-art solvers in accurately capturing the underlying physics.
References
[1] L.A. Richards, Capillary conduction of liquids through porous mediums, Physics, 1931, 1(5): 318-333.
[2] K. Mitra, I. Pop, A modified l-scheme to solve nonlinear diffusion problems, Computers & Mathematics with Applications, 2019, 77(6): 1722-1738.
[3] F. List, F. Radu, A study on iterative methods for solving Richardâs equation, Computational Geoscience, 2016, 20: 341-353.
[4] N. Suciu, D. Illiano, A. Prechtel, F. A. Radu, Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media, Advances in Water Resources, 2021, 152: 103935.