388 research outputs found
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
A "well-balanced" finite volume scheme for blood flow simulation
We are interested in simulating blood flow in arteries with a one dimensional
model. Thanks to recent developments in the analysis of hyperbolic system of
conservation laws (in the Saint-Venant/ shallow water equations context) we
will perform a simple finite volume scheme. We focus on conservation properties
of this scheme which were not previously considered. To emphasize the necessity
of this scheme, we present how a too simple numerical scheme may induce
spurious flows when the basic static shape of the radius changes. On contrary,
the proposed scheme is "well-balanced": it preserves equilibria of Q = 0. Then
examples of analytical or linearized solutions with and without viscous damping
are presented to validate the calculations. The influence of abrupt change of
basic radius is emphasized in the case of an aneurism.Comment: 36 page
To Split or Not to Split, That Is the Question in Some Shallow Water Equations
In this paper we analyze the use of time splitting techniques for solving
shallow water equation. We discuss some properties that these schemes should
satisfy so that interactions between the source term and the shock waves are
controlled. This paper shows that these schemes must be well balanced in the
meaning expressed by Greenberg and Leroux [5]. More specifically, we analyze in
what cases it is enough to verify an Approximate C-property and in which cases
it is required to verify an Exact C-property (see [1], [2]). We also include
some numerical tests in order to justify our reasoning
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
A limiter-based well-balanced discontinuous Galerkin method for shallow-water flows with wetting and drying: Triangular grids
A novel wetting and drying treatment for second-order Runge-Kutta
discontinuous Galerkin (RKDG2) methods solving the non-linear shallow water
equations is proposed. It is developed for general conforming two-dimensional
triangular meshes and utilizes a slope limiting strategy to accurately model
inundation. The method features a non-destructive limiter, which concurrently
meets the requirements for linear stability and wetting and drying. It further
combines existing approaches for positivity preservation and well-balancing
with an innovative velocity-based limiting of the momentum. This limiting
controls spurious velocities in the vicinity of the wet/dry interface. It leads
to a computationally stable and robust scheme -- even on unstructured grids --
and allows for large time steps in combination with explicit time integrators.
The scheme comprises only one free parameter, to which it is not sensitive in
terms of stability. A number of numerical test cases, ranging from analytical
tests to near-realistic laboratory benchmarks, demonstrate the performance of
the method for inundation applications. In particular, super-linear
convergence, mass-conservation, well-balancedness, and stability are verified
SWASHES: a compilation of Shallow Water Analytic Solutions for Hydraulic and Environmental Studies
Numerous codes are being developed to solve Shallow Water equations. Because
there are used in hydraulic and environmental studies, their capability to
simulate properly flow dynamics is critical to guarantee infrastructure and
human safety. While validating these codes is an important issue, code
validations are currently restricted because analytic solutions to the Shallow
Water equations are rare and have been published on an individual basis over a
period of more than five decades. This article aims at making analytic
solutions to the Shallow Water equations easily available to code developers
and users. It compiles a significant number of analytic solutions to the
Shallow Water equations that are currently scattered through the literature of
various scientific disciplines. The analytic solutions are described in a
unified formalism to make a consistent set of test cases. These analytic
solutions encompass a wide variety of flow conditions (supercritical,
subcritical, shock, etc.), in 1 or 2 space dimensions, with or without rain and
soil friction, for transitory flow or steady state. The corresponding source
codes are made available to the community
(http://www.univ-orleans.fr/mapmo/soft/SWASHES), so that users of Shallow
Water-based models can easily find an adaptable benchmark library to validate
their numerical methods.Comment: 40 pages There are some errors in the published version. This is a
corrected versio
The VOLNA code for the numerical modelling of tsunami waves: generation, propagation and inundation
A novel tool for tsunami wave modelling is presented. This tool has the
potential of being used for operational purposes: indeed, the numerical code
\VOLNA is able to handle the complete life-cycle of a tsunami (generation,
propagation and run-up along the coast). The algorithm works on unstructured
triangular meshes and thus can be run in arbitrary complex domains. This paper
contains the detailed description of the finite volume scheme implemented in
the code. The numerical treatment of the wet/dry transition is explained. This
point is crucial for accurate run-up/run-down computations. Most existing
tsunami codes use semi-empirical techniques at this stage, which are not always
sufficient for tsunami hazard mitigation. Indeed the decision to evacuate
inhabitants is based on inundation maps which are produced with this type of
numerical tools. We present several realistic test cases that partially
validate our algorithm. Comparisons with analytical solutions and experimental
data are performed. Finally the main conclusions are outlined and the
perspectives for future research presented.Comment: 47 pages, 27 figures. Other author's papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutykh
An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs
We extend the entropy stable high order nodal discontinuous Galerkin spectral
element approximation for the non-linear two dimensional shallow water
equations presented by Wintermeyer et al. [N. Wintermeyer, A. R. Winters, G. J.
Gassner, and D. A. Kopriva. An entropy stable nodal discontinuous Galerkin
method for the two dimensional shallow water equations on unstructured
curvilinear meshes with discontinuous bathymetry. Journal of Computational
Physics, 340:200-242, 2017] with a shock capturing technique and a positivity
preservation capability to handle dry areas. The scheme preserves the entropy
inequality, is well-balanced and works on unstructured, possibly curved,
quadrilateral meshes. For the shock capturing, we introduce an artificial
viscosity to the equations and prove that the numerical scheme remains entropy
stable. We add a positivity preserving limiter to guarantee non-negative water
heights as long as the mean water height is non-negative. We prove that
non-negative mean water heights are guaranteed under a certain additional time
step restriction for the entropy stable numerical interface flux. We implement
the method on GPU architectures using the abstract language OCCA, a unified
approach to multi-threading languages. We show that the entropy stable scheme
is well suited to GPUs as the necessary extra calculations do not negatively
impact the runtime up to reasonably high polynomial degrees (around ). We
provide numerical examples that challenge the shock capturing and positivity
properties of our scheme to verify our theoretical findings
- …