Implementing the Water, HEat and Transport model in GEOframe (WHETGEO-1D v.1.0): algorithms, informatics, design patterns, open science features, and 1D deployment

This paper presents WHETGEO and its 1D deployment: a new physically based model simulating the water and energy budgets in a soil column. The purpose of this contribution is twofold. First, we discuss the mathematical and numerical issues involved in solving the Richardson–Richards equation, conventionally known as the Richards equation, and the heat equation in heterogeneous soils. In particular, for the Richardson–Richards equation (R2) we take advantage of the nested Newton–Casulli–Zanolli (NCZ) algorithm that ensures the convergence of the numerical solution in any condition. Second, starting from numerical and modelling needs, we present the design of software that is intended to be the first building block of a new customizable land-surface model that is integrated with process-based hydrology. WHETGEO is developed as an open-source code, adopting the object-oriented paradigm and a generic programming approach in order to improve its usability and expandability. WHETGEO is fully integrated into the GEOframe/OMS3 system, allowing the use of the many ancillary tools it provides. Finally, the paper presents the 1D deployment of WHETGEO, WHETGEO-1D, which has been tested against the available analytical solutions presented in the Appendix.

Optimizing Water Consumption in Richards’ Equation Framework with Step-Wise Root Water Uptake: A Simplified Model

This work arises from the need of exploring new features for modeling and optimizing water consumption in irrigation processes. In particular, we focus on water flow model in unsaturated soils, accounting also for a root water uptake term, which is assumed to be discontinuos in the state variable. We investigate the possibility of accomplishing such optimization by computing the steady solutions of a $$\theta$$ θ -based Richards equation revised as equilibrium points of the ODEs system resulting from a numerical semi-dicretization in the space; after such semi-discretization, these equilibrium points are computed exactly as the solutions of a linear system of algebraic equations: the case in which the equilibrium lies on the threshold for the uptake term is of particular interest, since the system considerably simplifies. In this framework, the problem of minimizing the water waste below the root level is investigated. Numerical simulations are provided for representing the obtained results. Article Highlights Root water uptake is modelled in a Richards’ equation framework with a discontinuous sink term. After a proper semidiscretization in space, equilibrium points of the resulting nonlinear ODE system are computed exactly. The proposed approach simplifies a control problem for optimizing water consumption.

A Mathematical Model for Transport and Growth of Microbes in Unsaturated Porous Soil

In this work, we develop a mathematical model for transport and growth of microbes by natural (rain) water infiltration and flow through unsaturated porous soil along the vertical direction under gravity and capillarity by coupling a system of advection diffusion equations (for concentration of microbes and their growth-limiting substrate) with the Richards equation. The model takes into consideration several major physical, chemical, and biological mechanisms. The resulting coupled system of PDEs together with their boundary conditions is highly nonlinear and complicated to solve analytically. We present both a partial analytic approach towards solving the nonlinear system and finding the main type of dynamics of microbes, and a full-scale numerical simulation. Following the auxiliary equation method for nonlinear reaction-diffusion equations, we obtain a closed form traveling wave solution for the Richards equation. Using the propagating front solution for the pressure head, we reduce the transport equation to an ODE along the moving frame and obtain an analytic solution for the history of bacteria concentration for a specific test case. To solve the system numerically, we employ upwind finite volume method for the transport equations and stabilized explicit Runge–Kutta–Legendre super-time-stepping scheme for the Richards equation. Finally, some numerical simulation results of an infiltration experiment are presented, providing a validation and backup to the analytic partial solutions for the transport and growth of bacteria in the soil, stressing the occurrence of front moving solitons in the nonlinear dynamics.

Barrier Longevity of NaCl-Laden Soil against Subterranean Termites in an Earth Embankment

Subterranean termite-induced damage to earth embankments in agricultural systems occurs globally. NaCl-laden soil barriers (NLSBs) are an environmentally sustainable termite control method, and have exhibited good potential in preventing termite-related tunneling damage in Zhejiang Province, China. The persistence of the NaCl concentration in NLSBs is a key characteristic for the long-term prevention of subterranean termite infestations. This study is a scientific attempt to estimate the field efficacy and barrier longevity of NLSBs in reservoir embankments based on the Richards equation and the convection–dispersion equation using HYDRUS (2D/3D). The observed and simulated NaCl concentrations at the end of a 1915-day simulation were compared. The results indicated that the proposed model performed well and can effectively characterize the water flow and salt transport in NLSBs. The salt desalination rate of the NLSB in the upstream slope was higher than that in the downstream slope, both of which were significantly higher than that at the embankment axis. Regardless of the type of embankment (homogeneous or core-wall), the barrier longevity of NaCl-laden soil against subterranean termites can reach 50 years with an optimized NaCl/soil ratio in different parts of the embankment.

Grain-Filling Characteristics in Extra-Large Panicle Type of Early-Maturing japonica/indica Hybrids

Early-maturing japonica/indica hybrids (EJIH) have recently been released, performing a yield potential of 13.5 t ha−1 and greater yield increase over conventional japonica rice (CJ) and hybrid indica rice (HI) in production. More spikelets per panicle and improved grain-filling efficiency underlined the basis for the superior yield performance of EJIH. However, few studies are available on the panicle traits and grain-filling characteristics of EJIH, as well as their differences to CJ and HI. In our study, two EJIH, two CJ, and two HI cultivars with similar growth patterns were grown in the same fields. EJIH had a 12.2–18.8% increased (p < 0.05) grain yield relative to CJ and HI, mainly attributed to their higher daily grain yield. Although it had a lower panicle per m2, EJIH exhibited 28.0–38.3% more (p < 0.05) spikelets per m2 from an increase of 58.0–87.8% (p < 0.05) in spikelets per panicle than CJ and HI. Compared with CJ and HI, EJIH had a higher single panicle weight and more grains in the six parts of the panicle, especially in the upper secondary branches (US) and middle secondary branches (MS). EJIH exhibited a higher leaf area index (LAI), leaf area duration (LAD), leaf photosynthetic rate, and SPAD values after heading, which helped increase shoot biomass weight at heading and maturity and post-heading biomass accumulation. For CJ and HI, the grain-filling dynamics of grains in the six parts were all well simulated by the Richards equation. For EJIH, the grain-filling dynamics of grains in the lower secondary branches (LS) were well fitted by the logistics equation, with the Richards equation simulating grain positioning on the other five parts. EJIH had a lower mean grain-filling rate (GRmean) and longer days and grain filling amounts (GFA) during early, middle, and late stages than CJ and HI. Our results suggest EJIH gave a yield advantage over CJ and HI through a higher daily grain yield. The panicle traits and grain-filling characteristics differed greatly among the three cultivar types. Compared with CJ and HI, EJIH had lower GRmean and higher days and more grains in the panicle during early, middle, and late stages, which contributed to an increased GFA after heading, improved filled-grain efficiency, and higher grain yield.

Evaluation of the vacuum infusion process objectives at the early stages of computer simulation

Increasing the quality and reliable reproducibility of large-size composite structures molding using the vacuum infusion method, which is gaining popularity in various industries, is achieved in practice through numerous tests by try and errors that require significant costs and time. The purpose of these tests is to determine the layout of the ports for the resin injection and vacuum supply, as well as the temperature regime that ensures the absence of isolated non-impregnated zones, the minimum porosity and the required reinforcement volume fraction in the composite. The proposed approach removes the simplifying assumptions used in commercial software for modeling the process, which reduce the accuracy of reconstruction of its dynamics and the sensitivity to the formation of unrepairable defects such as dry spots. It involves multiphysics modeling of resin filling in a porous preform by describing the resin front dynamics by the phase field equation, pressure distribution in an unsaturated porous medium by the Richards equation, the evolution of the degree of cure by the convection / diffusion / thermokinetics equation, and thermal processes by the heat transfer equation using modified models of viscosity, the diffusion coefficient of the degree of cure, the boundary condition for the vacuum port. To reduce the finite element computation time of the investigated variants of the process, which is necessary for its computer optimization, the predictive partial sub-criteria were used, which give a reliable prediction before the beginning of the resin gel and solidification. Due to this, a gain in computation time is 30-50% with a significant prediction accuracy of quality objectives and the presence of possible defects.

Multiscale Multiphysics Modeling of the Infiltration Process in the Permafrost

In this work, we design a multiscale simulation method based on the Generalized Multiscale Finite Element Method (GMsFEM) for numerical modeling of fluid seepage under permafrost condition in heterogeneous soils. The complex multiphysical model consists of the coupled Richards equation and the Stefan problem. These problems often contain heterogeneities due to variations of soil properties. For this reason, we design coarse-grid spaces for the multiphysical problem and design special algorithms for solving the overall problem. A numerical method has been tested on two- and three-dimensional model problems. A a quasi-real geometry with a complex surface is considered for the three-dimensional case. We demonstrate the efficiency and accuracy of the proposed method using several representative numerical results.