Well-balanced finite difference WENO schemes for the blood flow model

The blood flow model maintains the steady state solutions, in which the flux gradients are non-zero but exactly balanced by the source term. In this paper, we design high order finite difference weighted non-oscillatory (WENO) schemes to this model with such well-balanced property and at the same time keeping genuine high order accuracy. Rigorous theoretical analysis as well as extensive numerical results all indicate that the resulting schemes verify high order accuracy, maintain the well-balanced property, and keep good resolution for smooth and discontinuous solutions

A limitation of the hydrostatic reconstruction technique for Shallow Water equations

Because of their capability to preserve steady-states, well-balanced schemes for Shallow Water equations are becoming popular. Among them, the hydrostatic reconstruction proposed in Audusse et al. (2004), coupled with a positive numerical flux, allows to verify important mathematical and physical properties like the positivity of the water height and, thus, to avoid unstabilities when dealing with dry zones. In this note, we prove that this method exhibits an abnormal behavior for some combinations of slope, mesh size and water height.Comment: 7 page

An analytical solution of Shallow Water system coupled to Exner equation

In this paper, an exact smooth solution for the equations modeling the bedload transport of sediment in Shallow Water is presented. This solution is valid for a large family of sedimentation laws which are widely used in erosion modeling such as the Grass model or those of Meyer-Peter & Muller. One of the main interest of this solution is the derivation of numerical benchmarks to valid the approximation methods

A well-balanced finite volume scheme for 1D hemodynamic simulations

We are interested in simulating blood flow in arteries with variable elasticity with a one dimensional model. We present a well-balanced finite volume scheme based on the recent developments in shallow water equations context. We thus get a mass conservative scheme which also preserves equilibria of Q=0. This numerical method is tested on analytical tests.Comment: 6 pages. R\'esum\'e en fran\c{c}ais : Nous nous int\'eressons \`a la simulation d'\'ecoulements sanguins dans des art\`eres dont les parois sont \`a \'elasticit\'e variable. Ceci est mod\'elis\'e \`a l'aide d'un mod\`ele unidimensionnel. Nous pr\'esentons un sch\'ema "volume fini \'equilibr\'e" bas\'e sur les d\'eveloppements r\'ecents effectu\'es pour la r\'esolution du syst\`eme de Saint-Venant. Ainsi, nous obtenons un sch\'ema qui pr\'eserve le volume de fluide ainsi que les \'equilibres au repos: Q=0. Le sch\'ema introduit est test\'e sur des solutions analytique

FullSWOF: A free software package for the simulation of shallow water flows

Numerical simulations of flows are required for numerous applications, and are usually carried out using shallow water equations. We describe the FullSWOF software which is based on up-to-date finite volume methods and well-balanced schemes to solve this kind of equations. It consists of a set of open source C++ codes, freely available to the community, easy to use, and open for further development. Several features make FullSWOF particularly suitable for applications in hydrology: small water heights and wet-dry transitions are robustly handled, rainfall and infiltration are incorporated, and data from grid-based digital topographies can be used directly. A detailed mathematical description is given here, and the capabilities of FullSWOF are illustrated based on analytic solutions and datasets of real cases. The codes, available in 1D and 2D versions, have been validated on a large set of benchmark cases, which are available together with the download information and documentation at http://www.univ-orleans.fr/mapmo/soft/FullSWOF/.Comment: 38 page

Determination of initial soil moisture for a small highly erodible mountain basin with TELEMAC

Hydrodynamic

A new gravity-driven runoff and erosion model for TELEMAC

Water Qualit

FullSWOF_Paral: Comparison of two parallelization strategies (MPI and SKELGIS) on a software designed for hydrology applications

In this paper, we perform a comparison of two approaches for the parallelization of an existing, free software, FullSWOF 2D (http://www. univ-orleans.fr/mapmo/soft/FullSWOF/ that solves shallow water equations for applications in hydrology) based on a domain decomposition strategy. The first approach is based on the classical MPI library while the second approach uses Parallel Algorithmic Skeletons and more precisely a library named SkelGIS (Skeletons for Geographical Information Systems). The first results presented in this article show that the two approaches are similar in terms of performance and scalability. The two implementation strategies are however very different and we discuss the advantages of each one.Comment: 27 page