Search results for " analytical solution"
showing 10 items of 12 documents
The MAST-edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media
2012
A novel methodology is proposed for the solution of the flow equation in a variably saturated heterogeneous porous medium. The computational domain is descretized using triangular meshes and the governing PDEs are discretized using a lumped in the edge centres numerical technique. The dependent unknown variable of the problem is the piezometric head. A fractional time step methodology is applied for the solution of the original system, solving consecutively a prediction and a correction problem. A scalar potential of the flow field exists and in the prediction step a MArching in Space and Time (MAST) formulation is applied for the sequential solution of the Ordinary Differential Equation of…
AN EFFICIENT SOLUTION OF HETEROGENEOUS ANISOTROPIC CONVECTION/DIFFUSION TRANSPORT PROBLEMS
2012
Discussion of “Unsteady Stage-Discharge Relationships for Sharp-Crested Weirs” by Firouz Ghasemzadeh, Salah Kouchakzadeh, and Gilles Belaud
2021
I would like to thank the authors for writing this interesting article dealing with unsteady stage-discharge relationships for sharp-crested weirs. The operation of triangular and rectangular sharp-crested weirs in unsteady flow conditions was experimentally investigated. Results indicated the presence of looped rating curves, with transposition of the rising and falling limbs compared to that commonly observed in stream gauge ratings. The authors found that the deviation between steady and unsteady flow rates in the looped rating curves depends on the weir type and the hydrograph gradient (i.e., the temporal depth variation), especially when the latter changes rapidly. Finally, they propos…
Overland flow generation on hillslopes of complex topography: analytical Solutions
2007
The analytical solution of the overland flow equations developed by Agnese et al. (2001; Hydrological Processes15: 3225–3238) for rectangular straight hillslopes was extended to convergent and divergent surfaces and to concave and convex profiles. Towards this aim, the conical convergent and divergent surfaces are approximated by a trapezoidal shape, and the overland flow is assumed to be always one-dimensional. A simple ‘shape factor’ accounting for both planform geometry and profile shape was introduced: for each planform geometry, a brachistochrone profile was obtained by minimizing a functional containing a slope function of the profile. Minima shape factors are associated with brachist…
Dual-Diameter Laterals in Center-Pivot Irrigation System
2022
Design strategies to enhance modern irrigation practices, reduce energy consumption, and improve water use efficiency and crop yields are fundamental for sustainability. Concerning Center-Pivot Irrigation Systems, different design procedures aimed at optimizing water use efficiency have been proposed. Recently, following a gradually decreasing sprinkler spacing along the pivot lateral with constant diameter and sprinkler flow rate, a new design method providing a uniform water application rate has been introduced. However, no suggestions were given to design multiple-diameter laterals characterized by different values of the inside pipe diameter. In this paper, first the previous design pro…
Linking the Kinetic Energy Fraction and Equivalent Length Method for Trickle Irrigation Design under Local Losses
2020
New methods using analytical relationships to design drip irrigation laterals and subunits have been introduced in recent years based on the assumption that minor losses can be neglected. This assumption could be relaxed by applying the equivalent method, which makes it possible to account for minor losses, such as those caused by emitter connections, through formulas based on the rationale that an equivalent length of the drip lateral produces the same losses. However, equivalent length formulas are empirical; thus, they do not necessarily cover the entire range of conditions in the real-world contexts in which the formulas will be applied, and their extrapolation could lead to erroneous r…
Analytical Solution of the Richards Equation under Gravity-Driven Infiltration and Constant Rainfall Intensity
2020
In the field of soil hydrology, the Richards equation is commonly used to model water flow in unsaturated soils. The high nonlinearity of the Richards equation makes it very challenging to solve analytically for situations that are meaningful in practical applications. In this paper, an exact and simple analytical solution of the Richards equation under gravity-driven infiltration and constant rainfall intensity is derived. First, the solution is presented under Torricelli's law, which mimics the soil hydraulic conductivity function and describes the emptying or filling process of a nonlinear water reservoir. Then, following a similar approach, the solution is extended to the Brooks and Cor…
MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes
2011
Abstract A new methodology for the solution of the 2D diffusive shallow water equations over Delaunay unstructured triangular meshes is presented. Before developing the new algorithm, the following question is addressed: it is worth developing and using a simplified shallow water model, when well established algorithms for the solution of the complete one do exist? The governing Partial Differential Equations are discretized using a procedure similar to the linear conforming Finite Element Galerkin scheme, with a different flux formulation and a special flux treatment that requires Delaunay triangulation but entire solution monotonicity. A simple mesh adjustment is suggested, that attains t…
A beam theory for layered composites subjected to uniformly distributed load
2015
A theory for multilayered composite beams undergoing transverse uniformly distributed loads is presented. The formulation starts by assuming a layer-wise kinematical model characterized by third order approximation of the axial displacements and fourth order approximation of the transverse displacements. By enforcing the point-wise balance equations as well as the interface continuity conditions, the layer-wise kinematical model is rewritten in terms of a set of generalized kinematical variables associated with the beam as a whole. Stress resultants are then obtained in terms of the generalized variables derivatives and of the normal stresses applied to the top and bottom surfaces of the la…
Simplified Model to Predict Runoff Generation Time for Well-Drained and Vegetated Soils
2016
The study of generation process of subsurface stormflow, typical of well-drained and high permeable soils, can be theoretically carried out by applying the continuity and the motion equations with the appropriate boundary conditions. However, difficulties and uncertainness on determining soil hydraulic properties and soil physics heterogeneities let this way not always feasible. In a different way, processes dynamic can be derived by the local scale through a coarse graining procedure, allowing to preserve medium motion character, while hydraulic fluctuation of the motion are lost. Following an approach as this, in this paper a simplified model to predict the runoff generation time, the so-…