Turbulence: Numerical Analysis, Modelling and Simulation

The problem of accurate and reliable simulation of turbulent flows is a central and intractable challenge that crosses disciplinary boundaries. As the needs for accuracy increase and the applications expand beyond flows where extensive data is available for calibration, the importance of a sound mathematical foundation that addresses the needs of practical computing increases. This Special Issue is directed at this crossroads of rigorous numerical analysis, the physics of turbulence and the practical needs of turbulent flow simulations. It seeks papers providing a broad understanding of the status of the problem considered and open problems that comprise further steps

Fluid-structure interaction and homogenization: from spatial averaging to continuous wavelet transform

Fluid-structure interaction (FSI) is classicaly modeled according a separated and local approach. It enables to take full advantage of the numerical methods specifically designed for each medium. However, it requires to take great care of the interface, and to exchange, between the algorithms, the information related to boundary conditions [1]. This treatment of the interface can quickly become too cumbersome in complex flow geometries, as in the industrial case study driving this work: an inviscid compressible flow interacting with French PWR fuel assemblies (Fig. 1a). In such specific applications, where the solid medium exhibits a discontinuous but periodic design, an homogenized and global approach is preferred [2]. Inspired by porous media [3, 4], multiphase flows, or Large Eddy Simulation (LES), it relies on a spatial averaging of the balance equations, thus allowing to remove all interfaces. However, such filtering techniques exhibit two major limitations: first, they do not deal properly with boundary conditions, due to the non-commutativity between the filtering operator and spatial derivatives, as detailed in [5, 6, 7] for LES; second, filtering implies loss of microscopic information, and thus requires a closure model to describe interactions between resolved and unresolved scales

Simulation of Richtmyer–Meshkov instability by sixth-order filter methods

Simulation of a 2-D Richtmyer–Meshkov instability (RMI), including inviscid, viscous and magnetic field effects was conducted comparing recently developed sixthorder filter schemes with various standard shock-capturing methods. The suppression of the inviscid gas dynamics RMI in the presence of a magnetic field was investigated by Samtaney and Wheatley et al. Numerical results illustrated here exhibit behavior similar to the work of Samtaney. Due to the different amounts and different types of numerical dissipation contained in each scheme, the structures and the growth of eddies for the chaotic-like inviscid gas dynamics RMI case are highly grid size and scheme dependent, even with many levels of refinement. The failure of grid refinement for all studied numerical methods extends to the viscous gas dynamics case for high Reynolds number. For lower Reynolds number, grid convergence has been achieved by all studied methods. To achieve similar resolution, standard shock-capturing methods require more grid points than filter schemes and yet the CPU times using the same grid for all studied methods are comparable

Adaptive filtering and limiting in compact high order methods for multiscale gas dynamics and MHD systems

The adaptive multistep linear and nonlinear filters for multiscale shock/turbulence gas dynamics and magnetohydrodynamics (MHD) flows of the authors are extended to include compact high order central differencing as the spatial base scheme. The adaptive mechanism makes used of multiresolution wavelet decomposition of the computed flow data as sensors for numerical dissipative control. The objective is to expand the work initiated in [Yee HC, Sjo¨green B. Nonlinear filtering in compact high order schemes. In: Proceedings of the 19th ICNSP and 7th APPTC conference; 2005; J Plasma Phys 2006;72:833–36] and compare the performance of adaptive multistep filtering in compact high order schemes with adaptive filtering in standard central (non-compact) schemes for multiscale problems containing shock waves

A new multifractal subgrid-scale model for large-eddy simulation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76563/1/AIAA-2002-983-903.pd

Numerical Simulation of Compressible Flows with Interfaces

Compressible interfacial flows exist in a variety of applications: reacting fronts, droplet break up, jets and sprays in high speed, shock passage in foams, etc. These flows behave in a complex multi-scale way including interface deformation, wave interface interaction and complex transport phenomena. In the first section, the interaction of a laminar flame with a compression wave is investigated. More precisely, the evolution of the burning interface is investigated and discussion over different compression waves and their effects on the flame geometry and burning rate are made. In the second part, a numeral framework for simulation of compressible multiphase flows using adaptive wavelet collocation method is developed. This study was originally motivated by the desire for a numerical tool capable of simulating the atomization process during start-up conditions in a supersonic combustor. To model such physics, the solver needs to handle high density ratios, transport terms and capillary effects. The multi-scale behaviour of these flows requires a multi-scale approach. Parallel Adaptive Wavelet Collocation Method (PAWCM) makes use of second generation wavelets to dynamically adapt the grid to localized structures in the flow in time and space. This approach allows the solution to be approximated using a subset of the points that would normally be used with a uniform grid scheme. Thus, computation on this subset is efficient and high levels of data compression is achieved