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
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Regular Article: A Fast Spectral Algorithm for Nonlinear Wave Equations with Linear Dispersion
Bengt Fornberg,Tobin A. Driscoll +1 more
TL;DR: In this paper, the authors use linearly implicit multistep methods, with the innovation of choosing different methods for different ranges in Fourier space-high accuracy at low wavenumbers and A-stability at high wenumbers.
Proceedings ArticleDOI
Advances in Pseudospectral Methods for Optimal Control
Fariba Fahroo,I. Michael Ross +1 more
TL;DR: In this article, the concept of primal-dual weighted interpolation is used to articulate a unifled theory for all pseudospectral (PS) methods for optimal control, which illuminates the previously hidden fact of the unit weight function implicit in the PS method based on Legendre-Gauss-Lobatto points.
Journal ArticleDOI
Direct numerical simulation of transition in a sharp cone boundary layer at Mach 6: fundamental breakdown
TL;DR: In this paper, the role of second-mode fundamental resonance, or (K-type) breakdown, is investigated using high-resolution "controlled” transition simulations for the laboratory conditions of the hypersonic transition experiments conducted at Purdue University.
Journal ArticleDOI
Numerical study of the instability of the Hartmann layer
TL;DR: In this article, the Hartmann thickness-based Reynolds number is calculated for an electrically conducting incompressible fluid between two parallel unbounded insulating walls affected by a wall-normal magnetic field (the Hartmann flow).
References
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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.
Journal ArticleDOI
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.