Numerical scheme for a water flow-driven forward stratigraphic model

• Published in: Computational geosciences Vol. 24; no. 1; pp. 37 - 60
• Main Authors: Peton, Nicolas, Cancès, Clément, Granjeon, Didier, Tran, Quang-Huy, Wolf, Sylvie
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.02.2020; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Computer simulation; Consumer goods; Earth and Environmental Science; Earth Sciences; Finite volume method; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Lakes; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Numerical Analysis; Original Paper; Rivers; Sciences of the Universe; Sediment; Sediment transport; Sediments; Simulators; Soil Science & Conservation; Stratigraphy; Transport processes; Water flow; Weather-limited erosion; Complementarity problem; Stratigraphic forward modeling; Laplacian; complementarity problem; p-Laplacian; weather-limited erosion; stratigraphic forward modeling
• ISSN: 1420-0597; 1573-1499
• DOI: 10.1007/s10596-019-09893-w

This paper is concerned with extending the stratigraphic model previously introduced by Eymard et al. (Int. J. Numer. Methods Eng. 60(2):527–548 2004 ) and subsequently studied by Gervais and her coauthors for the simulation of large-scale transport processes of sediments, subject to an erosion constraint. Two major novelties are considered: (i) the diffusion law relating the flux of sediments and the slope of the topography is now nonlinear and involves a p -Laplacian with p > 2 in order for landscape evolutions to be more realistic; (ii) the sediment transport is now intertwined with the water flows due to lakes and rivers via a direct coupling at the continuous PDE level, which avoids empirical algorithms at the discrete level such as MFD (multiple flow directions) at the price of additional p -Laplacians. Aimed at enriching the capabilities of IFPEN’s simulator, these sophistications entail the construction of a new finite volume scheme, the details of which are supplied. The physical model is validated through several test cases. Finally, a further extension of the model to the case of multiple lithologies is presented, along with numerical results.