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Mathematical and numerical analysisof a stratigraphic model

Published online by Cambridge University Press:  15 August 2004

Véronique Gervais  and
Roland Masson
Véronique Gervais
Affiliation:
Institut Français du Pétrole, 1 et 4 avenue de Bois Préau, 92852 Rueil Malmaison Cedex, France. [email protected].
Roland Masson
Affiliation:
Institut Français du Pétrole, 1 et 4 avenue de Bois Préau, 92852 Rueil Malmaison Cedex, France. [email protected].
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Abstract

In this paper, we consider a multi-lithology diffusion model used in stratigraphic modelling to simulate large scale transport processes of sediments described as a mixture of L lithologies. This model is a simplified one for which the surficial fluxes are proportional to the slope of the topography and to a lithology fraction with unitary diffusion coefficients.The main unknowns of the system are the sediment thickness h, the L surface concentrations $c_i^s$ in lithology i of the sediments at the top of the basin, and the L concentrations c i in lithology i of the sediments inside the basin. For this simplified model, the sediment thickness decouples from the other unknowns and satisfies a linear parabolic equation. The remaining equations account for the mass conservation of the lithologies, and couple, for each lithology, a first order linear equation for $c_i^s$ with a linear advection equation for c i for which $c_i^s$ appears as an input boundary condition. For this coupled system, a weak formulation is introduced which is shown to have a unique solution. An implicit finite volume scheme is derived for which we show stability estimates and the convergence to the weak solution of the problem.

Keywords

Finite volume methodstratigraphic modellinglinear first order equationsconvergence analysislinear advection equationunique weak solutionadjoint problem.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 4 , July 2004 , pp. 585 - 611
Copyright
© EDP Sciences, SMAI, 2004

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