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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A parametric analysis of reduced order models of viscous flows in turbomachinery
TL;DR: In this paper, a cascade of NACA-5506 airfoils is numerically investigated to show that reduced order models with only 35 degrees of freedom accurately predict the unsteady response of the full model with approximately 6000 degrees offreedom in the subsonic regime, for a broad range of Mach numbers.
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Multi-channel simulation of regeneration in honeycomb monolithic diesel particulate filters
TL;DR: In this paper, a multichannel DPF simulator was used to study the regeneration process over the entire spatial domain of the diesel particulate <er and the dynamics of hot spots induced by localized external energy deposition.
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Solution of Lane–Emden type equations using Legendre operational matrix of differentiation
TL;DR: An efficient numerical method is developed for solving linear and nonlinear Lane–Emden type equations using Legendre operational matrix of differentiation based on differentiation matrix of Legendre polynomial.
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The Fourier-Finite-Element Method for Poisson's Equation in Axisymmetric Domains with Edges
TL;DR: In this article, the Fourier-finite-element method was applied to the Dirichlet problem of the Poisson equation in axisymmetric domains with reentrant edges.
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Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation
TL;DR: In this article, an efficient numerical method for solving space fractional order diffusion equation is presented based on shifted Chebyshev polynomials of the second kind where the fractional derivatives are expressed in terms of Caputo type.
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.
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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.