Review of numerical solution of Richardson–Richards equation for variably saturated flow in soils

2019 ◽  
Vol 6 (5) ◽  
Author(s):  
Yuanyuan Zha ◽  
Jinzhong Yang ◽  
Jicai Zeng ◽  
Chak‐Hau M. Tso ◽  
Wenzhi Zeng ◽  
...  
Keyword(s):  
Numerical Solution ◽  
Richards Equation ◽  
Saturated Flow

scholarly journals Numerical analysis of coupled hydrosystems based on an object-oriented compartment approach

2008 ◽  
Vol 10 (3) ◽  
pp. 227-244 ◽  
Author(s):  
Olaf Kolditz ◽  
Jens-Olaf Delfs ◽  
Claudius Bürger ◽  
Martin Beinhorn ◽  
Chan-Hee Park
Keyword(s):  
Numerical Solution ◽  
Land Surface ◽  
Overland Flow ◽  
Drainage Basin ◽  
Spatial Scales ◽  
Shallow Water Equation ◽  
Object Oriented ◽  
Richards Equation ◽  
Saturated Flow ◽  
Flow Processes

In this paper we present an object-oriented concept for numerical simulation of multi-field problems for coupled hydrosystem analysis. Individual (flow) processes modelled by a particular partial differential equation, i.e. overland flow by the shallow water equation, variably saturated flow by the Richards equation and saturated flow by the groundwater flow equation, are identified with their corresponding hydrologic compartments such as land surface, vadose zone and aquifers, respectively. The object-oriented framework of the compartment approach allows an uncomplicated coupling of these existing flow models. After a brief outline of the underlying mathematical models we focus on the numerical modelling and coupling of overland flow, variably saturated and groundwater flows via exchange flux terms. As each process object is associated with its own spatial discretisation mesh, temporal time-stepping scheme and appropriate numerical solution procedure. Flow processes in hydrosystems are coupled via their compartment (or process domain) boundaries without giving up the computational necessities and optimisations for the numerical solution of each individual process. However, the coupling requires a bridging of different temporal and spatial scales, which is solved here by the integration of fluxes (spatially and temporally). In closing we present three application examples: a benchmark test for overland flow on an infiltrating surface and two case studies – at the Borden site in Canada and the Beerze–Reusel drainage basin in the Netherlands.

scholarly journals Fast and Robust Numerical Solution of the Richards Equation in Homogeneous Soil

2011 ◽  
Vol 49 (6) ◽  
pp. 2576-2597 ◽  
Author(s):  
Heiko Berninger ◽  
Ralf Kornhuber ◽  
Oliver Sander
Keyword(s):  
Numerical Solution ◽  
Richards Equation ◽  
Homogeneous Soil

scholarly journals Analysis free surface of nonlinear seepage using the MQRBF method

2021 ◽  
Vol 233 ◽  
pp. 03042
Author(s):  
Yan SU ◽  
Yan SU ◽  
Zhi-ming ZHENG ◽  
Cheng-yu GU ◽  
Long-teng ZHANG
Keyword(s):  
Free Surface ◽  
Numerical Solution ◽  
Solution Process ◽  
Earth Dam ◽  
Richards Equation ◽  
Boundary Values ◽  
Base Function ◽  
Trefftz Method ◽  
Transient Problem ◽  
Radial Base Function

In order to solve the characteristics of low accuracy and slow efficiency in traditional numerical solution the free surface problem, the multiquardatic radial base function collocation method(MQ RBF) is used to analyze the constant seepage and unsteady seepage of the homogeneous earth dam. Computation of transient problem of free surface of earth dam by the linear derivation of Richards equation. The results show that the calculation accuracy of the MQRBF is higher than that of the traditional numerical method. The solution process does not involve numerical integral calculation and grid reorganization, which greatly reduces the calculation amount. Compared with the Trefftz method, it has the advantage of solving boundary values and internal values at the same time. It is not limited by the solution of the Laplace equation, and its application is wider and simpler.

Numerical solution of Richards’ equation of water flow by generalized finite differences

2018 ◽  
Vol 101 ◽  
pp. 168-175 ◽  
Author(s):  
C. Chávez-Negrete ◽  
F.J. Domínguez-Mota ◽  
D. Santana-Quinteros
Keyword(s):  
Numerical Solution ◽  
Water Flow ◽  
Finite Differences ◽  
Richards Equation

scholarly journals Development and evaluation of a variably saturated flow model in the global E3SM Land Model (ELM) version 1.0

2018 ◽  
Vol 11 (10) ◽  
pp. 4085-4102 ◽  
Author(s):  
Gautam Bisht ◽  
William J. Riley ◽  
Glenn E. Hammond ◽  
David M. Lorenzetti
Keyword(s):  
Soil Moisture ◽  
Flow Model ◽  
Scale Model ◽  
Richards Equation ◽  
Benchmark Problems ◽  
Spatially Explicit ◽  
Grid Cells ◽  
Saturated Flow ◽  
Near Surface ◽  
Computational Performance

Abstract. Improving global-scale model representations of near-surface soil moisture and groundwater hydrology is important for accurately simulating terrestrial processes and predicting climate change effects on water resources. Most existing land surface models, including the default E3SM Land Model (ELMv0), which we modify here, routinely employ different formulations for water transport in the vadose and phreatic zones. Clark et al. (2015) identified a variably saturated Richards equation flow model as an important capability for improving simulation of coupled soil moisture and shallow groundwater dynamics. In this work, we developed the Variably Saturated Flow Model (VSFM) in ELMv1 to unify the treatment of soil hydrologic processes in the unsaturated and saturated zones. VSFM was tested on three benchmark problems and results were evaluated against observations and an existing benchmark model (PFLOTRAN). The ELMv1-VSFM's subsurface drainage parameter, fd, was calibrated to match an observationally constrained and spatially explicit global water table depth (WTD) product. Optimal spatially explicit fd values were obtained for 79 % of global 1.9∘ × 2.5∘ grid cells, while the remaining 21 % of global grid cells had predicted WTD deeper than the observationally constrained estimate. Comparison with predictions using the default fd value demonstrated that calibration significantly improved predictions, primarily by allowing much deeper WTDs. Model evaluation using the International Land Model Benchmarking package (ILAMB) showed that improvements in WTD predictions did not degrade model skill for any other metrics. We evaluated the computational performance of the VSFM model and found that the model is about 30 % more expensive than the default ELMv0 with an optimal processor layout. The modular software design of VSFM not only provides flexibility to configure the model for a range of problem setups but also allows for building the model independently of the ELM code, thus enabling straightforward testing of the model's physics against other models.

scholarly journals Numerical Solution of the Two-Dimensional Richards Equation Using Alternate Splitting Methods for Dimensional Decomposition

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1780
Author(s):  
Dariusz Gąsiorowski ◽  
Tomasz Kolerski
Keyword(s):  
Numerical Solution ◽  
Water Resource Management ◽  
Subsurface Flow ◽  
Seepage Flow ◽  
Accurate Method ◽  
Agricultural Science ◽  
Richards Equation ◽  
Two Dimensional ◽  
Computation Process ◽  
Dimensional Splitting

Research on seepage flow in the vadose zone has largely been driven by engineering and environmental problems affecting many fields of geotechnics, hydrology, and agricultural science. Mathematical modeling of the subsurface flow under unsaturated conditions is an essential part of water resource management and planning. In order to determine such subsurface flow, the two-dimensional (2D) Richards equation can be used. However, the computation process is often hampered by a high spatial resolution and long simulation period as well as the non-linearity of the equation. A new highly efficient and accurate method for solving the 2D Richards equation has been proposed in the paper. The developed algorithm is based on dimensional splitting, the result of which means that 1D equations can be solved more efficiently than as is the case with unsplit 2D algorithms. Moreover, such a splitting approach allows any algorithm to be used for space as well as time approximation, which in turn increases the accuracy of the numerical solution. The robustness and advantages of the proposed algorithms have been proven by two numerical tests representing typical engineering problems and performed for typical properties of soil.

Sign in / Sign up

Export Citation Format

Share Document