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High-order spectral element methods for the simulation of compressible turbulent flows

Abstract : This thesis is focused on the application of high-order methods to compressible turbulent flows. Aspects such as numerical dissipation/dispersion, dynamic Sub-Grid Scale modelling, shock-capturing techniques and compressibility effects on turbulence modelling are thoroughly discussed. An innovative generalisation of standard spectral analyses techniques applied to high-order methods is first presented. Spectral analyses of high-order methods are normally based on the numerical discretisation of the one-dimensional linear advection equation. In the present work, such approach has been generalised for non-constant advection velocities to gain more meaningful insights about high-order numerical discretisations of non-linear equations, such as Navier-Stokes or Euler equations. Numerical experiments have been conducted to highlight the role played by numerical fluxes and order of approximation for Spectral Difference and FR-DG methods. The informations gathered from spectral analyses are then used to present the Spectral Element Dynamic Model. The SEDM has been developed by Chapelier & Lodato to link numerical dissipation, which represents a typical build-in feature of spectral element methods, and classical explicit SGS dissipation within the framework of Large-Eddy Simulations of turbulent flows. A series of relevant transitional turbulent flows are then considered to better evaluate the performance of the SEDM in more complex conditions. Namely, a zero-pressure-gradient flow over a flat plate and a low-Reynolds SD7003 airfoil simulation. Within the framework of compressible flows, an innovative low dissipative bulk-based artificial viscosity shock-capturing technique is presented and analysed in detail. Numerical simulations in one to three dimensions, inviscid and viscous, laminar and turbulent flows are considered to provide a sufficiently wide range of flow configurations where the proposed model performs well. In particular, in comparison with another widely diffused artificial viscosity model based on a laplacian regularisation. The bulk-based artificial viscosity provides, in fact, considerably reduced levels of artificial dissipation of vortical structures, keeping, at the same time, the simulation stable. Finally, in the last part of the manuscript, the coexistence of all the up-mentioned investigations and models presented throughout the thesis is studied for more complex compressible turbulent flows. Among these, the transonic flow around an RAE2822 airfoil and the interaction between a turbulent boundary layer with a 24˚ compression ramp have been simulated using an LES approach, where the SEDM has been coupled with the proposed bulk-based AV technique. Both simulations provided results in good agreement with other simulations and experiments, certifying the robustness and reliability of the combined effect of the two models. In the end, in order to generalise even more the SEDM to more compressible applications, a Direct Numerical Simulation study for a compression/expansion ramp configuration has been performed. The impact of the spherical part of the SGS tensor (i.e., the turbulent kinetic energy), often not explicitly modelled for weakly compressible flows, appeared to have a relevant role in kinetic energy transfer. The SGS dissipation term has shown to be directly connected to the local levels of compressibility, identified by the velocity dilatation field. Compressions motions are more likely to experience classical direct kinetic energy cascade, whereas expansions promote back-scatter phenomena. All the contributions, ideas and investigations presented in this thesis represent the first step toward a unified LES model able to handle, at the same time, both turbulence under-resolution and shock-waves with techniques and strategies specifically tailored for high-order numerical schemes.
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Submitted on : Wednesday, October 27, 2021 - 2:10:18 PM
Last modification on : Tuesday, November 9, 2021 - 10:42:11 AM


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  • HAL Id : tel-03405449, version 2


Niccolo Tonicello. High-order spectral element methods for the simulation of compressible turbulent flows. Fluid mechanics [physics.class-ph]. Normandie Université, 2021. English. ⟨NNT : 2021NORMR046⟩. ⟨tel-03405449v2⟩



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