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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Rational Chebyshev pseudospectral approach for solving Thomas–Fermi equation
Kourosh Parand,Mehdi Shahini +1 more
TL;DR: In this paper, a pseudospectral method for solving the Thomas-Fermi equation is proposed based on rational Chebyshev pseudo-spectral method, which reduces the solution to the solution of a system of algebraic equations.
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An Integrated Prognostics Method Under Time-Varying Operating Conditions
TL;DR: An integrated prognostics method considering a time-varying operating condition, which integrates physical gear models and sensor data, and a polynomial chaos expansion (PCE) collocation method is applied in computing the likelihood function in the Bayesian inference and the predicted failure time distribution.
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Numerical simulation of fluid-structure interaction with the volume penalization method
TL;DR: A novel scheme for the numerical simulation of fluid-structure interaction problems that extends the volume penalization method, a member of the family of immersed boundary methods, to take into account flexible obstacles, and shows how the introduction of a smoothing layer allows for arbitrary motion of the deformable obstacle.
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Iterative and direct Chebyshev collocation spectral methods for one-dimensional radiative heat transfer
Ben-Wen Li,Ya-Song Sun,Yang Yu +2 more
TL;DR: In this article, the Chebyshev collocation spectral method for one-dimensional radiative heat transfer equation with participating media is presented; and sequentially the iterative and direct solvers are developed.
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Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence
TL;DR: In this paper, the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number PrM over a large range, namely 0.01≤PrM≤10.
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.