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
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Widnall instabilities in vortex pairs
Denis Sipp,Laurent Jacquin +1 more
TL;DR: In this paper, the authors analyzed the cooperative three-dimensional short-wave instabilities developing on concentrated vortex dipoles that have been obtained by means of two-dimensional direct numerical simulations and showed that the instability may occur whenever two Kelvin waves exist with the same frequency ω, the same axial wavenumber k and with azimuthal wavenumbers m and m+2.
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One- and two-dimensional travelling wave solutions in gas-fluidized beds
TL;DR: In this paper, both one-and two-dimensional travelling wave solutions of the ensemble-averaged equations of motion for gas and particles in fluidized beds have been computed using numerical continuation techniques as well as bifurcation theory.
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On the Horton–Rogers–Lapwood convective instability with vertical vibration: Onset of convection
Gérald Bardan,Abdelkader Mojtabi +1 more
TL;DR: In this article, the authors present a numerical and analytical study of diffusive convection in a rectangular saturated porous cell heated from below and subjected to high frequency vibration, where the configuration of the Horton-Rogers-Lapwood problem is adopted.
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Transverse dynamics of dispersive Alfvén waves. I. Direct numerical evidence of filamentation
D. Laveder,T. Passot,P. L. Sulem +2 more
TL;DR: In this paper, the three-dimensional dynamics of a monochromatic wave propagating along an ambient magnetic field is simulated by direct numerical integration of the Hall-magnetohydrodynamics equations, in spite of the presence of competing, possibly linearly dominant, instabilities that in some instances distort the above structures.
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Polynomial particular solutions for certain partial differential operators
TL;DR: In this article, a variant of the Dual Reciprocity Method (DRM) is used for solving boundary value problems based on approximating source terms by polynomials other than the traditional basis functions.
References
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Book
Navier-Stokes Equations
TL;DR: Schiff's base dichloroacetamides having the formula OR2 PARALLEL HCCl2-C-N ANGLE R1 in which R1 is selected from the group consisting of alkenyl, alkyl, alkynyl and alkoxyalkyl; and R2 is selected by selecting R2 from the groups consisting of lower alkylimino, cyclohexenyl-1 and lower alkynyl substituted cycloenenyl -1 as discussed by the authors.
Journal ArticleDOI
A spectral element method for fluid dynamics: Laminar flow in a channel expansion
TL;DR: In this article, a spectral element method was proposed for numerical solution of the Navier-Stokes equations, where the computational domain is broken into a series of elements, and the velocity in each element is represented as a highorder Lagrangian interpolant through Chebyshev collocation points.
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Numerical Simulation of Turbulent Flows
TL;DR: In this article, the Navier-Stokes equations are used to model the evolution of a turbulent mixing layer and turbulent channel flow in incompressible Newtonian fluids. And the results of simulations of homogeneous turbulence in uniform shear are presented graphically and discussed graphically.
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Spectral methods for problems in complex geometries
TL;DR: In this paper, a new iteration procedure is introduced to solve the full matrix equations resulting from spectral approximations to nonconstant coefficient boundary-value problems in complex geometries, and the work required to solve these spectral equations exceeds that of solving the lowest-order finite-difference approximation to the same problem by only O(N log N).
Improved turbulence models based on large eddy simulation of homogeneous, incompressible turbulent flows
TL;DR: In this paper, a subgrid scale similarity model is developed that can account for system rotation and the main effect of rotation is to increase the transverse length scales in the rotation direction, and thereby decrease the rates of dissipation.