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Conditions limites de sortie pour les méthodes de time-splitting appliquées aux équations Navier-Stokes / Outflow boundary conditions for time-splitting methods applied to Navier-Stokes equationsPoux, Alexandre 07 December 2012 (has links)
La simulation d’écoulements incompressibles pose de nombreuses difficultés. Une première est la question de savoir comment traiter la contrainte d’incompressibilité et le couplage vitesse/pression afin d’obtenir une solution précise à moindre coût. Pour cela, nous nous intéressons en particulier à deux méthodes de time splitting : la correction de pression et la correction de vitesse. Une seconde difficulté porte sur des conditions limites de sortie. Nous nous intéressons ici à deux d’entre elles : la condition limite de traction et la condition limite d’Orlanski. Après avoir détaillé les difficultés pouvant apparaître lors de l’implémentation des méthodes de time-splitting, nous proposons une nouvelle implémentation de la condition limite de traction qui permet d’améliorer les ordres de convergence obtenus. Nous nous intéressons ensuite à la condition limite d’Orlanski qui nécessite une certaine vitesse d’advection C dans la direction normale à la limite dont nous proposons ici une nouvelle définition. Nos propositions sont confrontées à de multiples écoulements physiques afin de valider leurs comportements : l’écoulement en aval d’une marche descendante, l’écoulement au niveau d’une bifurcation,l’écoulement autour d’un obstacle et des écoulements de Poiseuille-Rayleigh-Bénard. / One of the understudied difficulties in the simulation of incompressible flows is how to treat the incompressibilityconstraint and the velocity/pressure coupling in order to obtain an accurate solution at low computationnalcost. In this context, we develop two methods: pressure-correction and velocity-correction. An anotherdifficulty is due to the boundary conditions. We study here two of them : the traction boundary condition andthe Orlanski boundary condition. After having developed the difficulties that appears when implementing timesplittingmethods, we propose a new way to enforce the traction boundary condition which improves the orderof convergence. Then we propose a new definition of the advective velocity C which is needed for the Orlanskiboundary condition. Our propositions are validated against multiple physical flows: flow over a backward facingstep, flow around a biffurcation, flow around an obstacle and several Poiseuille-Rayleigh-Bénard flows.
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Characterization of nonlinearity parameters in an elastic material with quadratic nonlinearity with a complex wave fieldBraun, Michael Rainer 19 November 2008 (has links)
This research investigates wave propagation in an elastic half-space with a
quadratic nonlinearity in its stress-strain relationship. Different boundary conditions
on the surface are considered that result in both one- and two-dimensional wave
propagation problems. The goal of the research is to examine the generation of
second-order frequency effects and static effects which may be used to determine
the nonlinearity present in the material. This is accomplished by extracting the
amplitudes of those effects in the frequency domain and analyzing their dependency
on the third-order elastic constants (TOEC). For the one-dimensional problems, both
analytical approximate solutions as well as numerical simulations are presented. For
the two-dimensional problems, numerical solutions are presented whose dependency
on the material's nonlinearity is compared to the one-dimensional problems. The
numerical solutions are obtained by first formulating the problem as a hyperbolic
system of conservation laws, which is then solved numerically using a semi-discrete
central scheme. The numerical method is implemented using the package CentPack.
In the one-dimensional cases, it is shown that the analytical and numerical solutions
are in good agreement with each other, as well as how different boundary conditions
may be used to measure the TOEC. In the two-dimensional cases, it is shown that
there exist comparable dependencies of the second-order frequency effects and static
effects on the TOEC. Finally, it is analytically and numerically investigated how
multiple reflections in a plate can be used to simplify measurements of the material
nonlinearity in an experiment.
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