Christian Tenaud

Evaluation of TVD high resolution schemes for unsteady viscous shocked flows

Abstract The goal of this study is to evaluate the accuracy of several high resolution total variation diminishing schemes in solving complex unsteady viscous shocked flows. Two types of discretization, namely a combined time and space discretization, and an independent time and space discretization are considered. Both methods are associated with several limiters, among which a more accurate new family of limiters depending on the local wave velocity. The accuracy properties of each scheme are first reviewed on inviscid 1D and 2D test cases, in order to establish a ranking with respect to their dissipative error. We then study the flow produced by the interaction of a reflected shock wave with the incident boundary layer in a shock tube. The calculations are performed for two values of the Reynolds number. At Re=200, convergence is attained and it is shown that the combined time and space discretization method converges faster. Good classical limiters do almost the same job as the new family of limiters. When the Reynolds number is increased to the value of 1000, the flow becomes much more complex. Although convergence is hard to reach, the close examination of the results leads us to conclude that the combined time and space discretization method associated with the new limiter gives from far the best results.

New Resolution Strategy for Multiscale Reaction Waves using Time Operator Splitting, Space Adaptive Multiresolution, and Dedicated High Order Implicit/Explicit Time Integrators

We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problem induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of steep spatial gradients in the reaction fronts, spatially very localized. In this paper, we introduce a new resolution strategy based on time operator splitting and space adaptive multiresolution in the context of very localized and stiff reaction fronts. The paper considers a high order implicit time integration of the reaction and an explicit one for the diffusion term in order to build a time operator splitting scheme that exploits efficiently the special features of each problem. Based on recent theoretical studies of numerical analysis such a strategy leads to a splitting time step which is restricted by neither the fastest scales in the source term nor by stability constraints of the diffusive steps but only by the physics of the phenomenon. We aim thus at solving complete models including all time and space scales within a prescribed accuracy, considering large simulation domains with conventional computing resources. The efficiency is evaluated through the numerical simulation of configurations which were so far out of reach of standard methods in the field of nonlinear chemical dynamics for two-dimensional spiral waves and three-dimensional scroll waves, as an illustration. Future extensions of the proposed strategy to more complex configurations involving other physical phenomena as well as optimization capability on new computer architectures are discussed.

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

This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a finite volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud V. Daru, C. Tenaud, J. Comput. Phys. (2004)]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The efficiency of the method is demonstrated on challenging one- and two-dimensional benchmarks.

MODELLING OF POLLUTANT DISPERSION IN URBAN STREET CANYONS BY MEANS OF A LARGE-EDDY SIMULATION APPROACH

Large-eddy simulation is used to study the flow dynamics and the concentration dispersion in urban Street canyons. This method is particularly used to investigate the two-dimensional characteristics of the concentration field established for flows perpendicular to the street with emissions released near the floor of the Street by motor vehicles. The aim of this work is to study the influence of the instantaneous flow on the concentration field. Our results show that, for a street that is twice as wide as it is high, the average statistical solution presents two counter-rotating whirls, in, agreement with previous experimental results. The concentration in the leeward region of the canyon, compared with the windward one, is significant when the wind is perpendicular to the axis of the canyon.

LES of spatially developing 3D compressible mixing layer

Abstract The spatial development of a turbulent compressible mixing layer is investigated by means of large eddy simulation (LES). The subgrid viscosity is represented by the so-called mixed-scale model, adapted to compressible flows. Two different shock capturing schemes and three sets of inlet white-noise perturbations are investigated. The comparison between numerical and experimental results gives an overall good agreement.

A time semi-implicit scheme for the energy-balanced coupling of a shocked fluid flow with a deformable structure

The objective of this work is to present a conservative coupling method between an inviscid compressible fluid and a deformable structure undergoing large displacements. The coupling method combines a cut-cell Finite Volume method, which is exactly conservative in the fluid, and a symplectic Discrete Element method for the deformable structure. A time semi-implicit approach is used for the computation of momentum and energy transfer between fluid and solid, the transfer being exactly balanced. The coupling method is exactly mass-conservative (up to round-off errors in the geometry of cut-cells) and exhibits numerically a long-time energy-preservation for the coupled system. The coupling method also exhibits consistency properties, such as conservation of uniform movement of both fluid and solid, absence of numerical roughness on a straight boundary, and preservation of a constant fluid state around a wall having tangential deformation velocity. The performance of the method is assessed on test cases involving shocked fluid flows interacting with two and three-dimensional deformable solids undergoing large displacements.

Numerical simulation of the turbulent separation reattachment flow around a thick flat plate

This work concerns the turbulent flow generated around a thick flat plate to study the relationship between instantaneous flow structures and the unsteady pressure field. LES results compare favorably to experiments thanks to using a high order scheme. Mean and fluctuating quantities are very well predicted in both the detachment and the reattachment regions. Dimensionless frequencies, characteristic of flapping and shedding phenomena, have also been recorded that are in agreement with experiments.

Adaptive Multiresolution Methods for the Simulation of Shocks/Shear Layer Interaction in Confined Flows

The main objective of this work is to study the ability of a multiresolution method based on wavelet approximation to predict unsteady shocked flows. A correct prediction of shock wave phenomena is often crucial in flow simulations for many industrial configurations such as in air intakes of supersonic vehicles or shock tube facilities where moving shock waves interact with shear layers. To capture these very fine and localized structures, many shock capturing schemes have been developed in the last decades that work with adequat robustness. However, shock wave/shear layer interactions generate unsteady vortical flows with separation that need adaptive multiresolution technics to achieve correct predictions.

High Resolution Monotonicity-Preserving Schemes for Unsteady Compressible Flows

This paper deals with the development of high order accurate schemes for the numerical simulation of unsteady compressible flows. It is shown that very accurate monotonicity preserving schemes can be constructed using a combined time-space discretization approach.

LES of a Three Dimensional Shock-Wave/Boundary Layer Interaction in a Channel Flow

This study deals with the L arge E ddy S imulation of a 3D unsteady shock wave/boundary layer interaction, in sight of turbomachinery applications. The simulation of a compressible flow through a 3D channel (ONERA) has been performed in LES, with a third order WENO scheme (Jiang, Shu, 1996) and the mixed scale model (Tenaud, Ta Phuoc, 1996). The flow has already been studied experimentally at ONERA (Cahen, 1995), and numerically with RANS modeling (Gerolymos, Vallet, 1997). The unsteady results obtained by LES within and downstream of the 3D interaction are presented and analyzed. The mean velocity profiles in the interaction zone, are then compared to both experiments and statistical numerical results.Copyright