One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

A dynamic subgrid‐scale eddy viscosity model

http://home.eps.hw.ac.uk/~ab226/tmp/implicit/lele_92.pdf

Compact finite difference schemes with spectral-like resolution

https://apps.dtic.mil/sti/pdfs/ADA189392.pdf

Efficient implementation of essentially non-oscillatory shock-capturing schemes,II

https://hal.archives-ouvertes.fr/hal-01513346/document

Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement

Fundamental aspects of spectral methods are introduced. Recent developments in spectral methods are reviewed with an emphasis on collocation techniques. Their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed. The key role that these methods play in the simulation of stability, transition, and turbulence is brought out. A perspective is provided on some of the obstacles that prohibit a wider use of these methods, and how these obstacles are being overcome.

Spectral Methods in Fluid Dynamics

Since the publication of ''Spectral Methods in Fluid Dynamics'' 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded. (orig.)

/pdf/spectral-methods-fundamentals-in-single-domains-10bktdhplo.pdf

Spectral Methods: Fundamentals in Single Domains

In search of reliable computational methods for cosmic flow problems, we apply several commonly used algorithms and one new algorithm, to a representative problem in galactic gas dynamics. A careful choice of the algorithm used in a calculation is found to be of the utmost importance in obtaining reliable results. Two methods most commonly employed in astronomy (the Beam scheme and FCT methods) prove to be highly unsuitable for our test problem. The penalty in programming effort and computer time per grid point required for the best second-order accurate codes tested is more than offset by the improvement in accuracy obtained and the possibility to reduce the number of points in a grid.

A comparative study of computational methods in cosmic gas dynamics

Low-Dissipation and Low-Dispersion Runge-Kutta Schemes for Computational Acoustics

It is shown that the dilatational terms that need to be modeled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of these dilatational terms in homogeneous turbulence is explored by asymptotic analysis of the compressible Navier-Stokes equations. A non-dimensional parameter which characterizes some compressible effects in moderate Mach number, homogeneous turbulence is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

https://ntrs.nasa.gov/api/citations/19900005197/downloads/19900005197.pdf

M. Y. Hussaini

Papers

Spectral Methods in Fluid Dynamics

Spectral Methods: Fundamentals in Single Domains

A comparative study of computational methods in cosmic gas dynamics

Low-Dissipation and Low-Dispersion Runge-Kutta Schemes for Computational Acoustics

The analysis and modelling of dilatational terms in compressible turbulence