Mathematical and numerical analysis of a stratigraphic model

Véronique Gervais; Roland Masson

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 38, Issue: 4, page 585-611
  • ISSN: 0764-583X

Abstract

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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 ci 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 ci 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.

How to cite

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Gervais, Véronique, and Masson, Roland. "Mathematical and numerical analysis of a stratigraphic model." ESAIM: Mathematical Modelling and Numerical Analysis 38.4 (2010): 585-611. <http://eudml.org/doc/194229>.

@article{Gervais2010,
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 ci 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 ci 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. },
author = {Gervais, Véronique, Masson, Roland},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite volume method; stratigraphic modelling; linear first order equations; convergence analysis; linear advection equation; unique weak solution; adjoint problem.},
language = {eng},
month = {3},
number = {4},
pages = {585-611},
publisher = {EDP Sciences},
title = {Mathematical and numerical analysis of a stratigraphic model},
url = {http://eudml.org/doc/194229},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Gervais, Véronique
AU - Masson, Roland
TI - Mathematical and numerical analysis of a stratigraphic model
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 4
SP - 585
EP - 611
AB - 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 ci 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 ci 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.
LA - eng
KW - Finite volume method; stratigraphic modelling; linear first order equations; convergence analysis; linear advection equation; unique weak solution; adjoint problem.
UR - http://eudml.org/doc/194229
ER -

References

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