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We have examined three problems involving steady flows of Navier-Stokes fluids. In each problem non-classical effects are considered. In the first two problems, we consider fluids which have bulk viscosities which are much larger than their shear viscosities. In the last problem, we examine steady supersonic flows of a Bethe-Zel'dovich-Thompson (BZT) fluid over a thin airfoil or turbine blade. BZT fluids are fluids in which the fundamental derivative of gasdynamics changes sign during an isentropic expansion or compression. In the first problem we consider the effects of large bulk viscosity on the structure of the inviscid approximation using the method of matched asymptotic expansions. When the ratio of bulk to shear viscosity is of the order of the square root of the Reynolds number we find that the bulk viscosity effects are important in the first corrections to the conventional boundary layer and outer inviscid flow. At first order the outer flow is found to be frictional, rotational, and non-isentropic for large bulk viscosity fluids. The pressure is found to have first order variations across the boundary layer and the temperature equation is seen to have two additional source terms at first order when the bulk viscosity is large. In the second problem, we consider the reflection of an oblique shock from a laminar flat plate boundary layer. The flow is taken to be two-dimensional, steady, and the gas model is taken to be a perfect gas with constant Prandtl number. The plate is taken to be adiabatic. The full Navier-Stokes equations are solved using a weighted essentially non-oscillatory (WENO) numerical scheme. We show that shock-induced separation can be suppressed once the bulk viscosity is large enough. In the third problem, we solve a quartic Burgers equation to describe the steady, two-dimensional, inviscid supersonic flow field generated by thin airfoils. The Burgers equation is solved using the WENO technique. Phenomena of interest include the partial and complete disintegration of compression shocks, the formation of expansion shocks, and the collision of expansion and compression shocks. / Ph. D.

Cette étude aborde différents schémas d'intégration temporelle en calcul dynamique, et leur capacité à dissiper les hautes fréquences numériques introduites par les discrétisation temporelle et spatiale. La discrétisation temporelle d'un problème de dynamique peut être réalisée par la Méthode des Différences Finies ou celle des Eléments Finis et plus particulièrement la méthode de Galerkin - discontinue. Les résultats sont alors perturbés par des oscillations parasites d'origine purement numérique et issues des discrétisations temporelle et spatiale. Des méthodes permettent de les amortir en dissipant de l'énergie. Les schémas explicites amortissants de Tchamwa - Wielgosz et de Bonelli sont tout d'abord comparés au traditionnel Bulk-viscosity sur des cas 1D et 3D axi-symétriques. Un algorithme de pilotage de l'amortissement pour le schéma de Tchamwa - Wielgosz est ensuite développé de manière à obtenir une efficacité amortissante optimale tout au long des calculs sans pour autant observer une baisse trop importante de l'énergie. L'utilisation des méthodes amortissantes sur des exemples numériques issus d'essais expérimentaux (essais aux Barres de Hopkinson, impact transversal d'une tôle) est enfin étudiée. Des conclusions de cette étude, citons tout d'abord que l'utilisation des méthodes amortissantes s'avère très efficace pour filtrer les oscillations parasites mais en dissipant généralement trop d'énergie, ce qui a motivé le développement d'un pilotage original de l'amortissement. Une seconde innovation réside dans l'étude d'un schéma temporel explicite de type éléments finis permettant d'aboutir à des résultats se rapprochant de la solution théorique discrétisée.

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The diploma thesis deals with pressure pulsations in pipeline system with dynamic muffler. There is presented original geometry of side-branch resonator. Pressure pulsations are solved by a created mathematical model, numerical simulations and verified by an experimental approach. The influence of dynamic and bulk viscosity is involved in derived governing equations. A system of nonlinear equations is solved by genetic algorithm and frequency dependent relationship of bulk viscosity of air is determined afterwards. The correct function of used pressure sensors is tested. The processing of experimental data is performed by the fast Fourier transform with coherent sampling. Finally, a comparison of analytical, numerical and experimental approaches is introduced for different geometric variants of presented muffler.