Abstract
In this paper, a numerical approximation method for the two-dimensional unsaturated soil water movement problem is established by using the discontinuous finite volume method. We prove the optimal error estimate for the fully discrete format. Finally, the reliability of the method is verified by numerical experiments. This method is not only simple to calculate, but also stable and reliable.
Highlights
The movement of water in soil is a very complicated problem
We focus on the mathematical model characteristics of the two-dimensional unsaturated water motion problem, and we mainly discuss the discontinuous finite volume element method of the problem
When we take A(u) = u8 + 1 and A(u) = u9 + 1, K(u) = cu10, we find that: when the nonlinear property of the nonlinear term A(u) and K(u) is strong, if the convection term is not dominant, as shown in Tables 5 and 8, the error orders of the L2-mode and H1-mode obtained are approximately equal to 2 and 1, respectively, which are consistent with the theoretical analysis; if the convection term is dominant, from Tables 6 and 7 and 9 and 10, the discontinuous finite volume element method is far from the theoretical analysis
Summary
The movement of water in soil is a very complicated problem. This paper mainly studies the water movement in furrow irrigation, that is, the water movement in the trapezoidal region to the soil diffusion on both sides and the infiltration of the underground pipeline into the surrounding soil. The numerical solutions of one-dimensional and two-dimensional soil water movement problems are given by the finite difference method in Ref.
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