107 research outputs found
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
Determination of initial soil moisture for a small highly erodible mountain basin with TELEMAC
Hydrodynamic
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
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
Parallelization of a relaxation scheme modelling the bedload transport of sediments in shallow water flow
In this work we are interested in numerical simulations for bedload erosion
processes. We present a relaxation solver that we apply to moving dunes test
cases in one and two dimensions. In particular we retrieve the so-called
anti-dune process that is well described in the experiments. In order to be
able to run 2D test cases with reasonable CPU time, we also describe and apply
a parallelization procedure by using domain decomposition based on the
classical MPI library.Comment: 19 page
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