Numerical simulation of shock waves interacting with multimaterial interface is immensely challenging, particularly when the embedded interface is retained as a sharp entity. The challenge lies in accurately capturing and representing the interface dynamics and the wave patterns at the interface. In this regard, the ghost fluid method has been successfully used to capture the interface conditions for both fluid-fluid and solid-fluid interfaces. However, the ghost fluid method results in over/underheating errors when shocks impact interfaces, and hence must be supplemented with numerical corrective measures to mitigate these errors. Such corrections typically fail for strong shock applications. Variants and extensions ofthe ghost fluid method have been proposed to remedy its shortcomings with mixed success. In this paper, the performance of approaches based on the ghost fluid method, in the case of strong shocks impinging on immersed solid boundaries in compressible flows, is evaluated. It is found that (from the viewpoint of simplicity, robustness, and accuracy) a reflective boundary condition used in conjunction with a local Riemann solver at the interface proves to be a good choice. The method is found to be stable, accurate, and robust for wide range problems involving strong shocks interacting with embedded solid objects.

Ghost Fluid Method for Strong Shock Interactions Part 2: Immersed Solid Boundaries

A cut-cell finite volume - finite element coupling approach for fluid-structure interaction in compressible flow

The proper orthogonal decomposition (P.O.D.) is applied to the flow in a differentially heated cavity. The fluid considered is air, and the aspect ratio of the cavity is 4. At a fixed Rayleigh number, P.O.D. empirical functions are extracted, and low-dimensional models are built and compared to the numerical simulation. Generally speaking, low-D models provide a coarse picture of the flow, which is also quick, cheap, and easy to understand. They can help pinpoint leading instability mechanisms. They are potentially key players in a number of applications such as optimization and control. Our goal in this study is to determine how well the flow can be represented by very low-dimensional models. Two moderately complex situations are examined. In the first case, at some distance from the bifurcation point, the dynamics can still be reduced down to two modes, although it is necessary to account for the effect of higher-order modes in the model. In the second case, farther away from the bifurcation, the flow is chaotic. A ten-dimensional model successfully captures the essential dynamics of the flow. The procedure was seen to be robust. It clearly illustrates the power of the P.O.D. as a reduction tool.

Low-order Models for the Flow in a Differentially Heated Cavity

An immersed boundary formulation for simulating high-speed compressible viscous flows with moving solids

The spatio-temporal dynamics of separation bubbles induced to form in a fully developed turbulent boundary layer (with Reynolds number based on momentum thickness of the boundary layer of 490) over a flat plate is studied via direct numerical simulations. Two different separation bubbles are examined: one induced by a suction–blowing velocity profile on the top boundary and the other by a suction-only velocity profile. The latter condition allows reattachment to occur without an externally imposed favourable pressure gradient and leads to a separation bubble more representative of those occurring over airfoils and in diffusers. The suction-only separation bubble exhibits a range of clearly distinguishable modes, including a high-frequency mode and a low-frequency ‘breathing’ mode that has been observed in some previous experiments. The high-frequency mode is well characterized by classical frequency scalings for a plane mixing layer and is associated with the formation and shedding of spanwise-oriented vortex rollers. The topology associated with the low-frequency motion is revealed by applying dynamic mode decomposition to the data from the simulations and is shown to be dominated by highly elongated structures in the streamwise direction. The possibility of Gortler instability induced by the streamwise curvature on the upstream end of the separation bubble as the underlying mechanism for these structures and the associated low frequency is explored.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/85BEE59DF935D3AB18E5770EBC5F8E7B/S002211201900911Xa.pdf/div-class-title-spatio-temporal-dynamics-of-turbulent-separation-bubbles-div.pdf

Spatio-temporal dynamics of turbulent separation bubbles

https://hal.archives-ouvertes.fr/hal-01163118/document

A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method

https://hal.archives-ouvertes.fr/hal-01413083/document

On wall pressure fluctuations and their coupling with vortex dynamics in a separated–reattached turbulent flow over a blunt flat plate

The present study aims at developing, in the context of compressible aerodynamic flows, a numerical method able to correctly predict flows around geometrically complex bodies without using curvilinear body fitted grid. The present work is based on the immersed boundary condition (IBC) technique. A theoretical work has then been undertaken on the IBC technique applied to compressible flows which allows us to overcome known problems and propose solutions in the context of moving solid wall boundaries. The numerical results have been obtained on 1D (moving piston on a fixed mesh) and 2D laminar compressible flows, with or without shock-wave around a curvilinear body: a circular cylinder. The numerical results favourably compare to those of the literature, for 2D unsteady viscous compressible flows.

http://documents.irevues.inist.fr/bitstream/handle/2042/36682/293.pdf?sequence=1

Méthode de frontière immérgée pour la simulation d'écoulements visqueux compressibles.

This study deals with the numerical predictions through Large-Eddy Simulation (LES) of the separated– reattached turbulent flow over a blunt flat plate for analyzing main coherent structure features and their relation to the unsteady pressure field. Compared to experiments, LES results very well predict mean and fluctuating pressure and velocity fields. Flapping, shedding as well as Kelvin-Helmholtz characteristic frequencies educed by present simulations are in very good agreement with experimental values generally admitted. These characteristic modes are also visible on unsteady pressure signals, even rather far away from the separation. Mots clefs : : LES ; schema de haute precision ; couche limite turbulente decollee

Simulation numérique du décollement et recollement turbulent autour d'une plaque plane épaisse

We propose a general explicit coupling method between a Finite Volume method for compressible ow and a rigid body. The coupling strategy is based on the idea of Embedded Boundary methods [14]. The uxes are computed everywhere in the Cartesian grid, and are modi ed at the solid boundaries to enforce uid mass conservation. The coupling between the uid and the solid is designed to ensure a balance in momentum and energy. We prove the exact numerical conservation of several simple uniform ows. An illustrative example of the lifto of a cylinder by a shock wave is presented and compared with existing results. Mots clefs : Volumes Finis ; Interaction Fluide-structure ; Frontières immergées

Virginie Daru

Papers

A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method

On wall pressure fluctuations and their coupling with vortex dynamics in a separated–reattached turbulent flow over a blunt flat plate

Méthode de frontière immérgée pour la simulation d'écoulements visqueux compressibles.

Simulation numérique du décollement et recollement turbulent autour d'une plaque plane épaisse

Un algorithme de couplage conservatif pour l'interaction fluide-structure dans le cas compressible