Mathematical and numerical analysis of a stratigraphic model

Gervais, Véronique; Masson, Roland

doi:10.1051/m2an:2004035

Gervais, Véronique ; Masson, Roland

ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 4, pp. 585-611.

Résumé

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.

MR Zbl | 1 citation dans Numdam

DOI : 10.1051/m2an:2004035

Classification : 35M10, 35L50, 35Q99, 65M12
Mots-clés : finite volume method, stratigraphic modelling, linear first order equations, convergence analysis, linear advection equation, unique weak solution, adjoint problem

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     title = {Mathematical and numerical analysis of a stratigraphic model},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {585--611},
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     year = {2004},
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     zbl = {1130.86315},
     language = {en},
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Gervais, Véronique; Masson, Roland. Mathematical and numerical analysis of a stratigraphic model. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 4, pp. 585-611. doi : 10.1051/m2an:2004035. http://www.numdam.org/articles/10.1051/m2an:2004035/

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