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A regularisation strategy for the two-dimensional active-layer model

Published online by Cambridge University Press:  10 April 2026

Víctor Chavarrías Open the ORCID record for Víctor Chavarrías [Opens in a new window]
Víctor Chavarrías*
Affiliation:
Deltares , Delft, The Netherlands
*
Corresponding author: Victor Chavarrias, victor.chavarrias@deltares.nl
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Abstract

The active-layer model used to account for mixed-size sediment morphodynamic processes may be ill-posed under certain circumstances. Well-posedness guarantees the existence of a unique solution continuously depending on the problem data. When a model becomes ill-posed, infinitesimal perturbations to a solution grow infinitely fast. Apart from the fact that this behaviour cannot represent a physical process, numerical simulations of an ill-posed model continue to change as the grid is refined. For this reason, ill-posed models cannot be used as predictive tools. There exists a regularisation strategy based on a preconditioning method that guarantees that the one-dimensional active-layer model is well-posed. Here, we show that the extension of this strategy to two dimensions does not regularise the model and we propose a different regularisation strategy based on diffusion that guarantees that both the one-dimensional and two-dimensional active-layer models are well-posed. We implement the strategy in Delft3D Flexible Mesh and show an application.

JFM classification

Geophysical and Geological Flows: River dynamics Geophysical and Geological Flows: Sediment transport Geophysical and Geological Flows: Shallow water flows

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JFM Papers
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Journal of Fluid Mechanics , Volume 1032 , 10 April 2026 , A48
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© The Author(s), 2026. Published by Cambridge University Press

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