The Experts below are selected from a list of 6741 Experts worldwide ranked by ideXlab platform
I S Pop - One of the best experts on this subject based on the ideXlab platform.
-
travelling wave solutions for the Richards Equation incorporating non equilibrium effects in the capillarity pressure
Nonlinear Analysis-real World Applications, 2018Co-Authors: C J Van Duijn, K Mitra, I S PopAbstract:The Richards Equation is a mathematical model for unsaturated flow through porous media. This paper considers an extension of the Richards Equation, where non-equilibrium effects like hysteresis and dynamic capillarity are incorporated in the relationship that relates the water pressure and the saturation. The focus is on travelling wave solutions, for which the existence is investigated first for the model including hysteresis and subsequently for the model including dynamic capillarity effects. In particular, such solutions may have non monotonic profiles, which are ruled out when considering standard, equilibrium type models, but have been observed experimentally. The paper ends with numerical experiments confirming the theoretical results.
Jiri Simunek - One of the best experts on this subject based on the ideXlab platform.
-
verification of numerical solutions of the Richards Equation using a traveling wave solution
Advances in Water Resources, 2007Co-Authors: Vitaly A Zlotnik, John L Nieber, Tiejun Wang, Jiri SimunekAbstract:Abstract Efforts to find solutions that can be used for verification of numerical techniques for solving the Richards Equation have generated a wealth of approximate and exact analytical solutions. Coefficients of this Equation involve two highly non-linear functions related to the soil water potential, the unsaturated hydraulic conductivity, and the soil water content. The known exact solutions for realistic flow geometries are commonly limited to simplified descriptions of unsaturated hydraulic properties, while the approximate solutions involve various simplifications that require additional verification. We present a technique, referred to as the “launch pad” technique, which is based on the traveling wave solution to generate an exact solution of the boundary value problem for the Richards Equation. The technique that is applicable to any descriptor of unsaturated hydraulic properties is illustrated on an application involving the infiltration of water into soils with properties described by Brooks–Corey and van Genuchten models. Examples of verification are presented for HYDRUS-1D, a popular numerical computer code for solving the Richards Equation.
Do-hun Lee - One of the best experts on this subject based on the ideXlab platform.
-
Testing a conceptual hillslope recession model based on the storage–discharge relationship with the Richards Equation
Hydrological Processes, 2007Co-Authors: Do-hun LeeAbstract:The conceptual recession model based on the storage–discharge relationship was proposed to account for the unsaturated–saturated water storage interaction. The recession model was formulated by combining the constitutive storage–discharge relationship with the integral balance Equation for unsaturated and saturated water storage. The functional form of the constitutive storage–discharge relationship was determined from the spatial integration of the Richards Equation. The performance of the recession model was tested by comparing with the solution of the Richards Equation for different simulation geometric shapes and soil types. The conceptual recession model incorporating the unsaturated–saturated water storage interaction was in good agreement with the recession response of the Richards Equation. However, the recession model that neglected the unsaturated–saturated water storage interaction was comparable to the Richards Equation only for soils with the weak interaction between unsaturated water storage and saturated water storage. This result suggests the important role of the unsaturated–saturated water storage interaction in the formulation of the recession process when the derivative of the functional relationship between the unsaturated water storage and saturated water storage becomes significant. Copyright © 2007 John Wiley & Sons, Ltd.
-
testing a conceptual hillslope recession model based on the storage discharge relationship with the Richards Equation
Hydrological Processes, 2007Co-Authors: Do-hun LeeAbstract:The conceptual recession model based on the storage–discharge relationship was proposed to account for the unsaturated–saturated water storage interaction. The recession model was formulated by combining the constitutive storage–discharge relationship with the integral balance Equation for unsaturated and saturated water storage. The functional form of the constitutive storage–discharge relationship was determined from the spatial integration of the Richards Equation. The performance of the recession model was tested by comparing with the solution of the Richards Equation for different simulation geometric shapes and soil types. The conceptual recession model incorporating the unsaturated–saturated water storage interaction was in good agreement with the recession response of the Richards Equation. However, the recession model that neglected the unsaturated–saturated water storage interaction was comparable to the Richards Equation only for soils with the weak interaction between unsaturated water storage and saturated water storage. This result suggests the important role of the unsaturated–saturated water storage interaction in the formulation of the recession process when the derivative of the functional relationship between the unsaturated water storage and saturated water storage becomes significant. Copyright © 2007 John Wiley & Sons, Ltd.
K Mitra - One of the best experts on this subject based on the ideXlab platform.
-
Traveling wave solutions for the Richards Equation with hysteresis
Ima Journal of Applied Mathematics, 2019Co-Authors: E El Behi-gornostaeva, K Mitra, Ben SchweizerAbstract:We investigate the one-dimensional non-equilibrium Richards Equation with play-type hysteresis. It is known that regularized versions of this Equation permit traveling wave solutions that show oscillations and, in particular, the physically relevant effect of a saturation overshoot. We investigate here the non-regularized hysteresis operator and combine it with a positive $\tau$-term. Our result is that the model has monotone traveling wave solutions. These traveling waves describe the behavior of fronts in a bounded domain. In a two-dimensional interpretation, the result characterizes the speed of fingers in non-homogeneous solutions.
-
travelling wave solutions for the Richards Equation incorporating non equilibrium effects in the capillarity pressure
Nonlinear Analysis-real World Applications, 2018Co-Authors: C J Van Duijn, K Mitra, I S PopAbstract:The Richards Equation is a mathematical model for unsaturated flow through porous media. This paper considers an extension of the Richards Equation, where non-equilibrium effects like hysteresis and dynamic capillarity are incorporated in the relationship that relates the water pressure and the saturation. The focus is on travelling wave solutions, for which the existence is investigated first for the model including hysteresis and subsequently for the model including dynamic capillarity effects. In particular, such solutions may have non monotonic profiles, which are ruled out when considering standard, equilibrium type models, but have been observed experimentally. The paper ends with numerical experiments confirming the theoretical results.
C J Van Duijn - One of the best experts on this subject based on the ideXlab platform.
-
travelling wave solutions for the Richards Equation incorporating non equilibrium effects in the capillarity pressure
Nonlinear Analysis-real World Applications, 2018Co-Authors: C J Van Duijn, K Mitra, I S PopAbstract:The Richards Equation is a mathematical model for unsaturated flow through porous media. This paper considers an extension of the Richards Equation, where non-equilibrium effects like hysteresis and dynamic capillarity are incorporated in the relationship that relates the water pressure and the saturation. The focus is on travelling wave solutions, for which the existence is investigated first for the model including hysteresis and subsequently for the model including dynamic capillarity effects. In particular, such solutions may have non monotonic profiles, which are ruled out when considering standard, equilibrium type models, but have been observed experimentally. The paper ends with numerical experiments confirming the theoretical results.
