Spatially-dependent and nonlinear fluid transport: coupling framework

• Autorzy: Jürgen Geiser
• Języki publikacji: EN

Abstrakty

EN

We introduce a solver method for spatially dependent and nonlinear fluid transport. The motivation is from transport processes in porous media (e.g., waste disposal and chemical deposition processes). We analyze the coupled transport-reaction equation with mobile and immobile areas. The main idea is to apply transformation methods to spatial and nonlinear terms to obtain linear or nonlinear ordinary differential equations. Such differential equations can be simply solved with Laplace transformation methods or nonlinear solver methods. The nonlinear methods are based on characteristic methods and can be generalized numerically to higher-order TVD methods [Harten A., High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 1983, 49(3), 357–393]. In this article we will focus on the derivation of some analytical solutions for spatially dependent and nonlinear problems which can be embedded into finite volume methods. The main contribution is to embed one-dimensional analytical solutions into multi-dimensional finite volume methods with the construction idea of mass transport [Geiser J., Mobile and immobile fluid transport: coupling framework, Internat. J. Numer. Methods Fluids, 2010, 65(8), 877–922]. At the end of the article we present some results of numerical experiments for different benchmark problems.

Słowa kluczowe

EN

Advection-reaction equation; Spatial and nonlinear transport; Laplace transformation; Analytical solutions; Finite volume methods

Kategorie tematyczne

• 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 35K57: Reaction-diffusion equations
• 35K15: Initial value problems for second-order parabolic equations
• 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 47F05: Partial differential operators (should also be assigned at least one other classification number in section 47)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 1
• Strony: 116-136

Daty

wydano

2012-02-01

online

2011-12-09

Twórcy

autor

Jürgen Geiser

• Humboldt Universität zu Berlin Unter den Linden 6

Bibliografia

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• [9] Geiser J., Mobile and immobile fluid transport: coupling framework, Internat. J. Numer. Methods Fluids, 2010, 65(8), 877–922 http://dx.doi.org/10.1002/fld.2225
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Identyfikatory

DOI

10.2478/s11533-011-0120-1