Numerical Tests of the Lookup Table Method in Solving Richards’ Equation for Infiltration and Drainage in Heterogeneous Soils

Mohammad Islam,Mario Putti,Claudio Paniconi

doi:10.3390/hydrology4030033

Abstract

The lookup table option, as an alternative to analytical calculation for evaluating the nonlinear heterogeneous soil characteristics, is introduced and compared for both the Picard and Newton iterative schemes in the numerical solution of Richards’ equation. The lookup table method can be a cost-effective alternative to analytical evaluation in the case of heterogeneous soils, but it has not been examined in detail in the hydrological modeling literature. Three layered soil test problems are considered, and the robustness and accuracy of the lookup table approach are assessed for uniform and non-uniform distributions of lookup points in the soil moisture retention curves. Results from the three one-dimensional test simulations show that the uniform distributed option gives improved convergence and robustness for the drainage problem compared to the non-uniform strategy. On the other hand, the non-uniform technique can be chosen for test problems involving flow into initially dry layered soils.

Highlights

Richards’ equation is a standard, commonly-used approach for describing flow in partially-saturated porous media
The main purposes of this first test case are: (i) to verify that we have correctly implemented the lookup table method; (ii) to assess whether the lookup table method is robust; and (iii) to compare the computational efficiency and accuracy of the lookup table approach against the analytical approach
We have shown that the lookup table method for evaluating the soil moisture retention curves in

Summary

Introduction

Richards’ equation is a standard, commonly-used approach for describing flow in partially-saturated porous media. One of the numerous varieties of Richards’ equation is based on the pressure head (ψ) formulation, which is the most commonly-used because it has the advantage of being applicable to both saturated and unsaturated conditions and accommodating heterogeneous soils In this approach, mass balance is guaranteed by evaluating the moisture content change in a time step directly from the change in the water pressure head [4]. In modeling unsaturated flow problems involving sharp wetting fronts, it has been shown to offer excellent mass balance [5] This technique is simple to employ in head-based codes, requiring only an additional source term. This approach may encounter difficulties in stability and convergence for a sharp wetting front [6,7,8,9].

Methods

Results

Conclusion