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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Turbulent Compressible Convection with Rotation. I. Flow Structure and Evolution
TL;DR: In this article, the effects of rotation on the flow structure within the convection, its evolution, and some consequences for mixing are examined. But the authors focus on the large-scale mean shear flows that are generated by convection.
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On near resonances and symmetry breaking in forced rotating flows at moderate Rossby number
Leslie M. Smith,Youngsuk Lee +1 more
TL;DR: In this paper, a series of reduced models of homogeneous, rotating flow at moderate Rossby numbers Ro 0.1 were studied, for which both numerical and physical experiments show the generation of quasi-two-dimensional vortices and symmetry breaking in favour of cyclones.
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On the Gibbs phenomenon IV: recovering exponential accuracy in a subinterval from a Gegenbauer partial sum of a piecewise analytic function
David Gottlieb,Chi-Wang Shu +1 more
TL;DR: In this paper, it was shown that if we are given the first N Gegenbauer expansion coefficients, based on C(x) with the weight function (1-x^2)-for any constant 0, of an L_1 function f(x), we can construct an exponentially convergent approximation to the point values of f (x) in any sub-interval in which the function is analytic.
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Effect of the inner core on the numerical solution of the magnetohydrodynamic dynamo
Ataru Sakuraba,Masaru Kono +1 more
TL;DR: In this paper, the magnetohydrodynamic dynamo applied to rapidly rotating spherical systems using fully nonlinear equations under Boussinesq approximation has been investigated under the same parameter conditions but for a spherical shell and a sphere.
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Resolution effects and scaling in numerical simulations of passive scalar mixing in turbulence
TL;DR: The effects of finite grid resolution on the statistics of small scales in direct numerical simulations of turbulent mixing of passive scalars are addressed in this paper, where simulations at resolution Δ x ≈ η B are preferred and give adequate results for many important quantities including the scalar dissipation intermittency exponent and structure functions at moderately high orders.
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.