General function bases moment models for suspended sediment with vertical profile of concentration
Abstract
We introduce a general hydrostatic shallow moment framework for suspended sediment transport with vertically varying horizontal velocity and concentration profiles. The formulation is constructed over arbitrary vertical functional bases that are numerically orthogonalised via the Gram-Schmidt algorithm. This approach allows the approximation spaces for the vertical profile to be adapted to the specific structure of each physical variable, where also the velocity and sediment concentration can be projected onto different functional spaces. To overcome the limitations due to the inherent oscillatory nature of global Legendre polynomials, we explore a specific continuous piecewise linear ℙ1 finite-element basis. Furthermore, non-uniform vertical partitions are considered, enabling an enhanced representation of the vertical profiles in specific regions. Numerical experiments involving boundary layers and suspended sediment transport demonstrate that the proposed framework is accurate to reproduce the expected vertical profiles. The improvement is particularly significant for sediment concentration profiles with sharp vertical variations, where polynomial reconstructions exhibit pronounced oscillations leading to physically meaningless profiles, whereas the ℙ1 bases produce a qualitatively accurate representation of the vertical profiles observed in the sedimentation processes.
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BibTeX
@misc{caballerocardenas2026general,
title = {{General function bases moment models for suspended sediment with vertical profile of concentration}},
author = {Celia Caballero-Cárdenas and José Garres-Díaz and Irene Gómez-Bueno and Tomás Morales de Luna},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29468},
eprint = {2610.29468},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29468},
}
RIS
TY - UNPB
TI - General function bases moment models for suspended sediment with vertical profile of concentration
AU - Celia Caballero-Cárdenas
AU - José Garres-Díaz
AU - Irene Gómez-Bueno
AU - Tomás Morales de Luna
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29468
UR - https://arxiv.org/abs/2610.29468
AB - We introduce a general hydrostatic shallow moment framework for suspended sediment transport with vertically varying horizontal velocity and concentration profiles. The formulation is constructed over arbitrary vertical functional bases that are numerically orthogonalised via the Gram-Schmidt algorithm. This approach allows the approximation spaces for the vertical profile to be adapted to the specific structure of each physical variable, where also the velocity and sediment concentration can be projected onto different functional spaces. To overcome the limitations due to the inherent oscillatory nature of global Legendre polynomials, we explore a specific continuous piecewise linear ℙ_1 finite-element basis. Furthermore, non-uniform vertical partitions are considered, enabling an enhanced representation of the vertical profiles in specific regions. Numerical experiments involving boundary layers and suspended sediment transport demonstrate that the proposed framework is accurate to reproduce the expected vertical profiles. The improvement is particularly significant for sediment concentration profiles with sharp vertical variations, where polynomial reconstructions exhibit pronounced oscillations leading to physically meaningless profiles, whereas the ℙ_1 bases produce a qualitatively accurate representation of the vertical profiles observed in the sedimentation processes.
ER -