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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On the coupling of hyperbolic and parabolic systems: analytical and numerical approach
F. Gastaldi,Alfio Quarteroni +1 more
TL;DR: In this paper, the authors consider the coupling of hyperbolic and parabolic systems in a domain Ω divided into two disjoint subdomains Ω+ and Ω−.
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Numerical experiments with the lid driven cavity flow problem
A. B. Cortes,Jan D. Miller +1 more
TL;DR: In this paper, the centerline velocity profiles obtained from the solution of the two-and three-dimensional representations of the lid driven cavity flow problem are compared for different Reynolds numbers.
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A cardinal approach for nonlinear variable-order time fractional Schrödinger equation defined by Atangana–Baleanu–Caputo derivative
TL;DR: In this paper, an operational matrix method based on the shifted Legendre cardinal functions for solving the nonlinear variable-order time fractional Schrodinger equation was proposed, where the unknown solution is separated into real and imaginary parts, and then these parts are expanded in terms of the shifted-legendre functions with undetermined coefficients, and the generated operational matrix is utilized to extract a system of nonlinear algebraic equations.
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Random sweeping effect in isotropic numerical turbulence
T. Sanada,V. Shanmugasundaram +1 more
TL;DR: In this paper, full numerical simulations of the Navier-Stokes equations for three-dimensional, stationary, and isotropic turbulence are used to study the scaling properties of two-time modal velocity correlations and to determine the dominant process in the decorrelation of the small scale velocities.
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MHD simulations and astrophysical applications
TL;DR: In this article, the basic features of the magnetohydrodynamics framework are described and a brief introduction to the physical processes listed above, namely: dynamo action, MHD turbulence, and magnetic reconnection are made.
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.