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Mathematical and numerical analysis of a stratigraphic model
Published online by Cambridge University Press: 15 August 2004
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.
Keywords
- 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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