Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2303.03801

A semi-implicit finite volume method for the Exner model of sediment transport

S. Avgerinos·M. J. Castro·E. Macca·G. Russo
View original source ↗Read source document ↗Export metadata ↓

Abstract

The aim of this work is to construct efficient finite volume schemes for the numerical study of sediment transport in shallow water, in the framework of the Exner model.In most cases, the velocity related to the sediment is much lower that the fluid velocity, which, in turn, may be much lower that the free-surface wave speed. Explicit methods that resolve all waves require small time steps due to the CFL stability restriction because of fast surface waves. Furthermore, if Rusanov flux is adopted, slow sediment waves may be affected by the large numerical diffusion. The objective of the present work is to drastically improve the efficiency in the computation of the evolution of the sediment by treating water waves implicitly, thus allowing much larger time steps than the one required by fully explicit schemes. The goal is reached by suitably semi-implicit schemes obtained by the use of implicit-explicit Runge-Kutta methods.

Explore related subjects

math.NAcs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

S. Avgerinos, M. J. Castro, E. Macca, G. Russo. 2023-03-07. A semi-implicit finite volume method for the Exner model of sediment transport. https://arxiv.org/abs/2303.03801

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fully spectral scheme for the linear BGK equation on the whole space

In this article, we design a fully spectral method in both space and velocity for a linear inhomogeneous kinetic equation with mass, momentum and energy conservation. We focus on the linear BGK equation with a confinement potential $Φ$, even if the method could be applied to different collision operators. It is based upon the projection on Hermite polynomials in velocity and orthonormal polynomials with respect to the weight $e^{-$Φ$}$ in space. The potential $Φ$ is assumed to be a polynomial. It is, to the author's knowledge, the first scheme which preserves hypocoercive behavior in addition to the conservation laws. These different properties are illustrated numerically on both quadratic and double well potential.

math.NA↗
arXiv2026

Inverse inequalities for kernel-based approximation on bounded domains and Riemannian manifolds

This paper establishes inverse inequalities for kernel-based approximation spaces defined on bounded Lipschitz domains in $\mathbb{R}^d$ and compact Riemannian manifolds. While inverse inequalities are well-studied for polynomial spaces, their extension to kernel-based trial spaces poses significant challenges. For bounded Lipschitz domains, we extend prior Bernstein inequalities, which only apply to a limited range of Sobolev orders, to the full range of lower and upper orders, and derive Nikolskii inequalities that bound $L_\infty$ norms by $L_2$ norms. For compact Riemannian manifolds, we focus on restricted kernels, which are defined as the restriction of positive definite kernels from the ambient Euclidean space to the manifold, and prove their counterparts.

math.NA↗
arXiv2026

Error Estimates for Hyperbolic Scaling Limits of Linear Kinetic Models on Networks

This paper studies linear discrete kinetic models on networks and their asymptotic behavior in the small Knudsen number limit. For coupling conditions at an n-edge junction under a symmetric formulation, we introduce a change of variables that reformulates the system into n independent initial-boundary value problems. The asymptotic expansions are then constructed and rigorously justified by deriving an error estimate based on the energy method.

math.NA↗