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Numerical solution of a nonstandard Darcy flow model

  • We consider a Darcy flow model with saturation-pressure relation extended with a dynamic term, namely, the time derivative of the saturation. This model was proposed in works of J.Hulshof and J.R.King (1998), S.M.Hassanizadeh and W.G.Gray (1993), F.Stauffer (1978). We restrict ourself to one spatial dimension and strictly positive initial saturation. For this case we transform the initial-boundary value problem into combination of elliptic boundary-value problem and initial value problem for abstract Ordinary Differential Equation. This splitting is rather helpful both for theoretical aspects and numerical methods.

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Author:Vsevolod Laptev
URN (permanent link):urn:nbn:de:hbz:386-kluedo-39331
Advisor:Helmut Neunzert, Aivars Zemitis
Document Type:Study Thesis
Language of publication:English
Publication Date:2014/11/23
Date of first Publication:1999/09/28
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2014/11/25
Tag:Abstract ODE; Dynamic capillary pressure; Local existence uniqueness; Porous flow
Number of page:III, 42
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Axx General topics / 35A01 Existence problems: global existence, local existence, non-existence
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Axx General topics / 35A02 Uniqueness problems: global uniqueness, local uniqueness, nonuniqueness
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Mxx Equations and systems of special type (mixed, composite, etc.) / 35M11 Initial value problems for equations of mixed type
65-XX NUMERICAL ANALYSIS / 65Jxx Numerical analysis in abstract spaces / 65J08 Abstract evolution equations
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L06 Multistep, Runge-Kutta and extrapolation methods
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Sxx Flows in porous media; filtration; seepage / 76S05 Flows in porous media; filtration; seepage
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 28.10.2014