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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Missing point estimation in models described by proper orthogonal decomposition
TL;DR: The effectiveness of the MPE method is demonstrated by applying it to a nonlinear computational fluid dynamic model of an industrial glass furnace and the Galerkin projection can be computed using only 25% of the spatial grid points without compromising the accuracy of the reduced model.
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Direct simulations of turbulent flow using finite-difference schemes
TL;DR: In this paper, a high-order accurate finite-difference approach is presented for calculating incompressible turbulent flow, which can be applied to complex geometries more easilty than highly accurate spectral methods.
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Pseudospectra of the Orr-Sommerfeld operator
TL;DR: The spectrum of the Orr–Sommerfeld operator consists of three branches and it is shown that the eigenvalues at the intersection of the branches are highly sensitive to perturbations and that the sensitivity increases dramatically with the Reynolds number.
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Exponential convergence and H‐c multiquadric collocation method for partial differential equations
TL;DR: The radial basis function (RBF) collocation method as discussed by the authors uses global shape functions to interpolate and collocatethe approximate solution of PDEs, which is a truly meshless method as compared to some of the so-calledmeshless or element-free element methods.
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Toward Planetesimals: Dense Chondrule Clumps in the Protoplanetary Nebula
TL;DR: In this paper, the authors outline a scenario that traces a direct path from freely floating nebula particles to the first 10-100 km sized bodies in the terrestrial planet region, producing planetesimals that have properties matching those of primitive meteorite parent bodies.
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.