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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Analysis of central and upwind compact schemes
TL;DR: In this article, central and upwind compact schemes for spatial discretization have been analyzed with respect to accuracy in spectral space, numerical stability and dispersion relation preservation, and some well-known compact schemes that were found to be G-K-S and time stable are shown to be unstable for selective length scales by this analysis.
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The effect of the formulation of nonlinear terms on aliasing errors in spectral methods
TL;DR: In this article, the effect on aliasing errors of the formulation of nonlinear terms, such as the convective terms in the Navier-Stokes equations of fluid dynamics, is examined.
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Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term
Hans Johnston,Jian-Guo Liu +1 more
TL;DR: Systematic numerical experiments indicate that a second order implicit time discretization of the viscous term, with the pressure and convective terms treated explicitly, is stable under the standard CFL condition.
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The method of uncertainty quantification and minimization using polynomial chaos expansions
David A. Sheen,Hai Wang +1 more
TL;DR: This work proposes the Method of Uncertainty Minimization using Polynomial Chaos Expansions (MUM-PCE) to quantify and constrain these uncertainties in the rate parameters of a well-characterized, detailed chemical model.
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Fast algorithms for computing the Boltzmann collision operator
Clément Mouhot,Lorenzo Pareschi +1 more
TL;DR: For a particular class of interactions, including the so-called hard spheres model in dimension three, this work is able to derive spectral methods that can be evaluated through fast algorithms based on a suitable representation and approximation of the collision operator.
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.