Convergence of a numerical scheme for stratigraphic modeling

摘要

In this paper, we consider a multilithology diffusion model used in the field of stratigraphic basin simulations to simulate large scale depositional 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 variables 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 ci for which c(i)(s) appears as an input boundary condition. For this coupled system, a weak formulation is introduced.The system is discretized by an implicit time integration and a cell centered finite volume method. This numerical scheme is shown to satisfy stability estimates and to converge, up to a subsequence, to a weak solution of the problem.