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 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 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

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 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.

scholarly journals Handling the water content discontinuity at the interface between layered soils within a numerical scheme

Soil Research ◽  
2005 ◽  
Vol 43 (8) ◽  
pp. 945 ◽  
Author(s):  
C. J. Matthews ◽  
F. J. Cook ◽  
J. H. Knight ◽  
R. D. Braddock
Keyword(s):  
Numerical Solution ◽  
Water Content ◽  
Numerical Scheme ◽  
Iterative Scheme ◽  
Method Of Lines ◽  
Soil Layer ◽  
Iterative Solution ◽  
Richards Equation ◽  
Layered Soils ◽  
Fine Soil

In general, the water content (θ) form of Richards’ equation is not used when modeling water flow through layered soil since θ is discontinuous across soil layers. Within the literature, there have been some examples of models developed for layered soils using the θ-form of Richards’ equation. However, these models usually rely on an approximation of the discontinuity at the soil layer interface. For the first time, we will develop an iterative scheme based on Newton’s method, to explicitly solve for θ at the interface between 2 soils within a numerical scheme. The numerical scheme used here is the Method of Lines (MoL); however, the principles of the iterative solution could be used in other numerical techniques. It will be shown that the iterative scheme is highly effective, converging within 1 to 2 iterations. To ensure the convergence behaviour holds, the numerical scheme will be tested on a fine-over-coarse and a coarse-over-fine soil with highly contrasting soil properties. For each case, the contrast between the soil types will be controlled artificially to extend and decrease the extent of the θ discontinuity. In addition, the numerical solution will be compared against a steady-state analytical solution and a numerical solution from the literature.

scholarly journals Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions

2014 ◽  
Vol 24 (05) ◽  
pp. 901-936 ◽  
Author(s):  
Heiko Berninger ◽  
Mario Ohlberger ◽  
Oliver Sander ◽  
Kathrin Smetana
Keyword(s):  
Surface Water ◽  
Numerical Experiments ◽  
Domain Boundary ◽  
Time Discretization ◽  
Richards Equation ◽  
Regularization Technique ◽  
Coupled Problem ◽  
Minimization Problems ◽  
Homogeneous Soil ◽  
Robin Boundary

We analytically and numerically analyze groundwater flow in a homogeneous soil described by the Richards equation, coupled to surface water represented by a set of ordinary differential equations (ODEs) on parts of the domain boundary, and with nonlinear outflow conditions of Signorini's type. The coupling of the partial differential equation (PDE) and the ODE's is given by nonlinear Robin boundary conditions. This paper provides two major new contributions regarding these infiltration conditions. First, an existence result for the continuous coupled problem is established with the help of a regularization technique. Second, we analyze and validate a solver-friendly discretization of the coupled problem based on an implicit–explicit time discretization and on finite elements in space. The discretized PDE leads to convex spatial minimization problems which can be solved efficiently by monotone multigrid. Numerical experiments are provided using the DUNE numerics framework.

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