arXiv subjects

Tomás Morales de Luna

Publications and source records attributed to Tomás Morales de Luna.

4 recordsLinked to original sources

arXiv2026

General function bases moment models for suspended sediment with vertical profile of concentration

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 $\mathbb{P}_1$ 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 $\mathbb{P}_1$ bases produce a qualitatively accurate representation of the vertical profiles observed in the sedimentation processes.

math.NA↗

arXiv2021

In-cell Discontinuous Reconstruction path-conservative methods for non conservative hyperbolic systems -- Second-order extension

We are interested in the numerical approximation of discontinuous solutions in non conservative hyperbolic systems. An extension to second-order of a new strategy based on in-cell discontinuous reconstructions to deal with this challenging topic is presented. This extension is based on the combination of the first-order in-cell reconstruction and the MUSCL-Hancock reconstruction. The first-order strategy allowed in particular to capture exactly the isolated shocks and this new second-order extension keep this property. We also set the basis of an extension to high-order methods following this in-cell methodology and a way for capturing exactly more than one shock. Several numerical tests are proposed to validate the methods for the Coupled-Burgers system, Gas dynamics equations in Lagrangian coordinates and the modified shallow water system.

math.NA↗

arXiv2020

Shallow Water Moment models for bedload transport problems

In this work a simple but accurate shallow model for bedload sediment transport is proposed. The model is based on applying the moment approach to the Shallow Water Exner model, making it possible to recover the vertical structure of the flow. This approach allows us to obtain a better approximation of the fluid velocity close to the bottom, which is the relevant velocity for the sediment transport. A general Shallow Water Exner moment model allowing for polynomial velocity profiles of arbitrary order is obtained. A regularization ensures hyperbolicity and easy computation of the eigenvalues. The system is solved by means of an adapted IFCP scheme proposed here. The improvement of this IFCP type scheme is based on the approximation of the eigenvalue associated to the sediment transport. Numerical tests are presented which deal with large and short time scales. The proposed model allows to obtain the vertical structure of the fluid, which results in a better description on the bedload transport of the sediment layer.

physics.flu-dyn↗

arXiv2020

A weakly non-hydrostatic shallow model for dry granular flows

A non-hydrostatic depth-averaged model for dry granular flows is proposed, taking into account vertical acceleration. A variable friction coefficient based on the $μ(I)$ rheology is considered. The model is obtained from an asymptotic analysis in a local reference system, where the non-hydrostatic contribution is supposed to be small compared to the hydrostatic one. The non-hydrostatic counterpart of the pressure may be written as the sum of two terms: one corresponding to the stress tensor and the other to the vertical acceleration. The model introduced here is weakly non-hydrostatic, in the sense that the non-hydrostatic contribution related to the stress tensor is not taken into account due to its complex implementation. A simple and efficient numerical scheme is proposed. It consists of a three-step splitting procedure, and it is based on a hydrostatic reconstruction. Two key points are: (i) the friction force has to be taken into account before solving the non-hydrostatic pressure. Otherwise, the incompressibility condition is not ensured; (ii) both the hydrostatic and the non-hydrostatic pressure are taken into account when dealing with the friction force. The model and numerical scheme are then validated based on several numerical tests, including laboratory experiments of granular collapse. The influence of non-hydrostatic terms and of the choice of the coordinate system (Cartesian or local) is analyzed. We show that non-hydrostatic models are less sensitive to the choice of the coordinate system. In general, the non-hydrostatic model introduced here much better reproduces granular collapse experiments compared to hydrostatic models. An important result is that the simulated mass profiles up to the deposit and the front velocity are greatly improved. As expected, the influence of the non-hydrostatic pressure is shown to be larger for small values of the slope.

physics.flu-dyn↗