000004965 001__ 4965
000004965 005__ 20170831220332.0
000004965 037__ $$aTAZ-TFM-2010-037
000004965 041__ $$aeng
000004965 1001_ $$aCaviedes Voullieme, Daniel Eduardo
000004965 24500 $$aNumerical simulation of one-dimensional transient vertical flow in variably saturated soils
000004965 260__ $$aZaragoza$$bUniversidad de Zaragoza$$c2010
000004965 506__ $$aby-nc-sa$$bCreative Commons$$c3.0$$uhttp://creativecommons.org/licenses/by-nc-sa/3.0/
000004965 500__ $$aResumen disponible también en español
000004965 520__ $$aWater flow in variably saturated (saturated/unsaturated) soils is commonly modeled by means of Richards' equation. This equation has no general analytical solution and the use of numerical approximations is necessary. It can be presented in three physically equivalent forms which are based on different variables and show different mathematical properties. In this work, these forms are derived from the general mathematical model and analyzed from a numerical perspective in order to understand the interactions between the differential equations and the numerical methods required in each case. The goals of this work are, on the one hand, to describe the physical and mathematical reasoning which leads to the formulation of the general mathemati- cal model of flow in porous media, the discussion of the concepts and assumptions which allow to develop Richards' equation, and on the other hand, to establish the properties and limitations of several numerical schemes to approximate the solutions of flows in variably saturated soils. The approach for the mathematical model is to average a microscopic, single- phase flow equation into a macroscopic scale which allows to describe porous media in a practical way, and to consider the necessary assumptions to state Richards' equation as a particular flow case. The porous media constitutive model completes the mathematical model. In this work the Mualem-van Genuchten model and some variants are included. For the numerical model, several schemes are developed for the 1D Richards' equation in the vertical direction. Explicit and implicit centered finite difference schemes are used in this work. The key numerical aspects of interest are those of mass conservation, stability and efficiency. Another key aspect, which is not only numerical is that of continuity from unsaturated into saturated regimes. The constitutive models affect the numerical schemes and some issues arise because of the high non-linearity of the functions, in particular the hydraulic conductivity function. Appropriate discretization of hydraulic conductivity for estimation of flux between numerical cells is a sensible issue wich has been studied by many authors and is treated in this work. All of these issues are analyzed individually and as interrelated problems in the schemes. Validation and test cases are presented and the response of the model to different problems and parameters is examined. From them, it is concluded that the explicit and the implicit schemes based on the mixed form of Richards' equation are better suited for unsaturated problems. For variably saturated problems, the implicit scheme based on the mixed form is the best choice, since the explicit model cannot solve saturation conditions. Conditional stability of the explicit model affects negatively its performance in certain cases, which also leads to the conclusion that the implicit scheme is more efficient and realiable.
000004965 521__ $$aMáster Universitario en Mecánica Aplicada
000004965 540__ $$aDerechos regulados por licencia Creative Commons
000004965 6531_ $$aRichards' equation
000004965 6531_ $$aUnsaturated soils
000004965 6531_ $$aPorous media
000004965 6531_ $$aFinite differences
000004965 6531_ $$aPartial differential equations
000004965 700__ $$aGarcía Navarro, Pilar$$edir.
000004965 7102_ $$aUniversidad de Zaragoza$$bCiencia y Tecnología de Materiales y Fluidos$$cMecánica de Fluidos
000004965 830__ $$aCPS
000004965 8560_ $$fdaxav@unizar.es
000004965 8564_ $$s2833079$$uhttps://zaguan.unizar.es/record/4965/files/TAZ-TFM-2010-037.pdf$$yMemoria (eng)$$zMemoria (eng)
000004965 909CO $$ooai:zaguan.unizar.es:4965$$ptrabajos-fin-master$$pdriver
000004965 950__ $$a
000004965 980__ $$aTAZ$$bTFM$$cCPS