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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Viscous instabilities in trailing vortices at large swirl numbers
David Fabre,Laurent Jacquin +1 more
TL;DR: In this article, a family of viscous instabilities existing in a range of parameters which are usually assumed to be stable, namely large swirl parameters (q > 1.5) and large Reynolds numbers, are studied numerically using an original and highly accurate Chebyshev collocation method.
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A comparison of efficiency and error convergence of multiquadric collocation method and finite element method
TL;DR: In this article, the authors demonstrate the efficiency and accuracy of the multiquadric collocation method as compared to the finite element method, and demonstrate by three examples that the accuracy achieved by the MQ solution cannot be rivaled by the FEM.
Three-dimensional filling flow into a model left ventricle
TL;DR: In this paper, a numerical study of the three-dimensional fluid dynamics inside a model left ventricle during diastole is presented, where the ventricles are modeled as a portion of a prolate spheroid with a moving wall, whose dynamics is externally forced to agree with a simplified waveform of the entering flow.
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A study of the coarsening in tin/lead solders
W. Dreyer,Wolfgang H. Müller +1 more
TL;DR: In this article, the authors present a model based on continuum theory to simulate the coarsening process observed during thermo-mechanical treatment of binary tin-lead solders, where Fourier transforms and spectral theory are used for the numerical treatment of the thermoelastic as well as of the diffusion problem encountered during phase separation in these alloys.
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.