Dans le cadre de l’équipe associée AMoSS, relatif au programme entre l’Inria et Taiwain, nous organisons une semaine de travail du 7 au 10 Juillet à Inria Sophia-Antipolis.
La journée du 8 juillet sera dédiée à des présentations et seront ouvertes à une plus large audience. Vous êtes cordialement invité à cette journée sur le thème des modèles de type « Shallow watter » et des schémas d’approximations associés.
Advanced Modeling on Shear Shallow Flows for Curved Topography:
Water and granular flows.
Annual Workshop of the Associated Team AMoSS.
July 8, 2015 at NRIA Sophia Antipolis Méditerranée
08H30-09H00
Introduction
B. Nkonga
Laboratoire de Mathématiques J.A. Dieudonné/Inria team CASTOR,
UMR n° 7351 CNRS Univ. de Nice – Sophia Antipolis, 06108 Nice
09H00-09H30
A new model of long dispersive waves on shear flows
Aix-Marseille Université, CNRS, UMR 7343, IUSTI, Marseille
09H45-10H15
Experimental observation on surface undulations over erodible bed
Yih-Chin Tai1, Chin-Kai Cheng1 and Chih-Yu Kuo2
1Dep. of Hydraulic and Ocean Engineering, National Cheng Kung Univ., 701 Tainan, Taiwan, ROC
<style= »text-align: center; »>2Research Center for Applied Sciences, Academia Sinica, 115 Taipei, Taiwan, ROC
<style= »text-align: center; »>E-mail: yctai@mail.ncku.edu.tw
With a smooth and fixed bottom, undular hydraulic jumps take place when the flow transits from a supercritical flow to a subcritical one, where the upstream Froude Number is slightly above unity. The surface oscillations by the undular hydraulic jumps are suspected to originate from the existence of non-hydrostatic pressure. Surface undulations are experimentally investigated in flows over erodible bottom, where a mixture layer of sand and water lies between the bottom and clear water layer. The experiments were conducted in a smooth-walled channel of 1.2 cm wide and 90 cm long. Through the techniques of image processing and particle image velocimetry (PIV), the velocity distributions in the clear water and mixture layers are measured. Different from the undular hydraulic jumps at fixed bottom, the velocity profiles at crests and troughs are of a similar shape. However, at erodible bed, the bottom is of undulation, of which a phase shift of 0.5p to the surface is observed. Remarkably, the interface between the clear water layer and mixture one is only slightly undular and in phase with the bottom undulation.
10H30-11H00
Modified shallow water equations for significant bathymetry variations
Laboratoire de Mathématiques J.A. Dieudonné
UMR n° 7351 CNRS Univ. de Nice – Sophia Antipolis, 06108 Nice
11H15-11H45
Well balanced ALE : simple (lazy mans’s) time dependent mesh adaptation for balance laws
M. Ruchiotto
Team CARDAMOM : Inria Bordeaux – Sud-Ouest, 200 Avenue de la Vieille Tour, 33405 Talence
11H45-12H15
A flexible approach for the numerical solution of the Green-Nagdhi equations
A.G. Filippini, M. Kazolea, M. Ricchiuto
Inria Bordeaux sud-Ouest, Team CARDAMOM -200 av. De la vielle tour, 33405 Talence cedex France
A flexible hybrid approach for the numerical solution of the Green-Nagdhi equations will be presented. The equations are re-written using an elliptic and a hyperbolic part. A two step solution procedure is then developed: In the elliptic phase the source term is computed by inverting the coercive operator associated to the dispersive effects and a in the hyperbolic phase the flow variables are evolved by solving the non-linear shallow water equations with all non-hydrostatic effects accounted for by the source computed in the elliptic phase. For the numerical discretization of the elliptic phase we use the standard C0 Galerkin finite element method while high order finite volume and stabilized finite element methods are used in
the hyperbolic phase. In order to obtain a robust embedding of wave breaking we evaluate two strategies where the equations are locally reverting to the non-linear shallow water equations to model energy dissipation in breaking regions. The discrete models obtained are thoroughly tested on benchmarks problems. The proposed strategy can be easily generalized on arbitrary unstructured meshes in the multidimensional case.
14H00-14H30
Gas kinetic scheme for anisotropic Savage-Hutter Model
C.Y. Kuo
Research Center for Applied Sciences, Academia Sinica, 115 Taipei, Taiwan, ROC
The gas-kinetic scheme is applied to the Savage-Hutter model. In this method, the continuum fluxes are calculated based on the pseudo particle motions that are relaxed from unequilibrium to equilibrium states. The processes are described by the Bhatnagar-Gross-Krook (BGK) equation. The benefit of this scheme is its capability to resolve shock discontinuities sharply and to handle the vacuum state without special treatments. Because the Savage-Hutter equation bears an anisotropic stress on the tangential space of the topography, the equilibrium distribution function of the microscopic particles are shown to be bi-Maxwellian. These anisotropic stresses are shown the key to preserve the coordinate objectivity in the Savage-Hutter model. The effect of the anisotropic stress is illustrated by two examples: an axisymmetric dam break and a finite mass sliding on an inclined planar chute. It is found that the propagation of the flow fronts significantly depends on the orientation of the principal axes of the tangential stresses.
14H45-15H15
Stabilized spectral element approximation of the Saint Venant system using the entropy viscosity technique
Laboratoire de Mathématiques J.A. Dieudonné/ Inria team CASTOR,
UMR n° 7351 CNRS Univ. de Nice – Sophia Antipolis, 06108 Nice
Because high-order methods are known to produce spurious oscillations in shocks, solving non-linear hyperbolic systems of conservation laws with high accuracy is a challenging task. Assuming that an entropy does exist for the considered physical problem, the entropy viscosity method (EVM) offers an elegant way to stabilize various numerical discretizations, including the standard Finite Element Method or Spectral Element Method (SEM) and even Fourier expansions. Here we consider the Saint Venant (shallow water) system, i.e. an approximation of the incompressible Euler equation widely used to describe river flows, inundation phenomena or erosion problems. We especially focus on physical problems that involve dry – wet transitions and address them successfully with the standard SEM stabilized with a variant of the EVM well suited for the treatment of dry zones.
15H00-15H30
On solitary waves for boussinesq’s type models
Team CARDAMOM : Inria Bordeaux – Sud-Ouest, 200 Avenue de la Vieille Tour, 33405 Talence
IPB, Institut Polytechnique de Bordeaux
15H45-16H15
Well-Balanced schemes.
Laboratoire de Mathématiques J.A. Dieudonné/Projet Inria Castor,
UMR n° 7351 CNRS Univ. de Nice – Sophia Antipolis, 06108 Nice
