Open AccessBook
Spectral Methods in Fluid Dynamics
M. Y. Hussaini,Thomas A. Zang +1 more
TLDR
Spectral methods have been widely used in simulation of stability, transition, and turbulence as discussed by the authors, and their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed.Abstract:
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.read more
Citations
More filters
Journal ArticleDOI
Compact finite difference schemes with spectral-like resolution
TL;DR: In this article, the authors present finite-difference schemes for the evaluation of first-order, second-order and higher-order derivatives yield improved representation of a range of scales and may be used on nonuniform meshes.
Journal ArticleDOI
Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement
TL;DR: In this article, the concept of isogeometric analysis is proposed and the basis functions generated from NURBS (Non-Uniform Rational B-Splines) are employed to construct an exact geometric model.
Book
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
TL;DR: In this article, the authors present a review of rigor properties of low-dimensional models and their applications in the field of fluid mechanics. But they do not consider the effects of random perturbation on models.
Journal ArticleDOI
Femtosecond filamentation in transparent media
Arnaud Couairon,André Mysyrowicz +1 more
TL;DR: In this paper, the main aspects of ultrashort laser pulse filamentation in various transparent media such as air (gases), transparent solids and liquids are introduced and discussed.
Book ChapterDOI
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
TL;DR: In this paper, the authors describe the construction, analysis, and application of ENO and WENO schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations, where the key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible.
References
More filters
Journal ArticleDOI
Planetary waves in the atmosphere
TL;DR: In this paper, a numerical method for solving the non-linear barotropic vorticity equation in spherical coordinates is presented, where the stream function is expressed as a sum of surface spherical harmonics and the harmonic tendency equations are used to find the flow pattern at a future time from a knowledge of the harmonic coefficients at an initial time.
Journal ArticleDOI
The structure of the vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields
John Kim,Parviz Moin +1 more
TL;DR: In this article, the bursting process is associated with well-organized horseshoe vortices inclined at about 45 degrees to the wall, and these vortical structures are identified by examining the vortex lines of three-dimensional, ensemble averaged vorticity fields.
Journal ArticleDOI
Direct numerical simulations of chemically reacting turbulent mixing layers
TL;DR: The results of direct numerical simulations of chemically reacting, turbulent mixing layers are presented in this article, and the simulation results are shown to be consistent with similarity theory, and are found to be in approximate agreement with laboratory data, even though there are no adjustable parameters in the method.
Journal ArticleDOI
The Fourier method for nonsmooth initial data
TL;DR: In this paper, the Fourier method is applied to very general linear hyperbolic Cauchy problems with nonsmooth initial data, and it is shown that applying appropriate smoothing techniques applied to the equation gives stability and that this smoothing combined with a certain smoothing of the initial data leads to infinite order accuracy away from the set of discontinuities of the exact solution modulo a small easily characterized exceptional set.
Journal ArticleDOI
A spectral collocation method for the Navier-Stokes equations
TL;DR: In this article, a Fourier-Chebyshev spectral method for the incompressible Navier-Stokes equations is described, which is applicable to a variety of problems including some with fluid properties which vary strongly both in the normal direction and in time.