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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An efficient 3-D spectral-element method for Schro/spl uml/dinger equation in nanodevice simulation
Joon-Ho Lee,Qing Huo Liu +1 more
TL;DR: Numerical results show that the SEM is an efficient alternative to conventional FEM and to the finite-difference method (FDM) for nanodevice simulation, and higher geometrical orders are essential for curved structures to achieve overall spectral accuracy.
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The spectral methods for parabolic Volterra integro-differential equations
TL;DR: This paper studies the numerical solutions to parabolic Volterra integro-differential equations in one-dimensional bounded and unbounded spatial domains and uses the algebraic mapping to transfer the problem on a bounded domain and then applies the presented approach for the bounded domain.
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Stability Margin Scaling Laws for Distributed Formation Control as a Function of Network Structure
TL;DR: For a given fixed number of vehicles, the scaling law can be improved significantly by employing a higher dimensional information graph and/or by introducing small asymmetry in the nominally symmetric proportional control gains.
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The sea surface pressure formulation of rigid lid models. Implications for altimetric data assimilation studies
TL;DR: The sea surface pressure formulation of the rigid lid primitive equation oceanic problem is reviewed and clarified in this paper, and a diagnostic relationship is found that relates the surface pressure to the barotropic and baroclinic components of the subsurface flow field.
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Modal Stability TheoryLecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013
TL;DR: In this article, a review of modal stability theory for parallel flows is presented, including temporal stability, spatial stability, phase velocity, group velocity, and spati-calculus.
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.
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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.