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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Magnetohydrodynamic (MHD) flows of viscoelastic fluids in converging/diverging channels
TL;DR: In this article, the applicability of magnetic fields for controlling hydrodynamic separation in Jeffrey-Hamel flows of viscoelastic fluids was investigated and a local similarity solution was found for laminar, two-dimensional flow obeying second-order/second-grade model as its constitutive equation with the assumption that the flow is symmetric and purely radial.
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Nonlinear higher-order spectral solution for a two-dimensional moving load on ice
TL;DR: In this paper, the nonlinear response of an infinite ice sheet to a moving load in the time domain in two dimensions, using a higher-order spectral method, was calculated, and it was shown that the non-linearity is due to the moving boundary, as well as the non linear term in Bernoulli's equation and the elastic plate equation.
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Investigation of the PSE approach for subsonic and supersonic hot jets. Detailed comparisons with LES and Linearized Euler Equations results
TL;DR: In this paper, a Parabolized Stability Equation (PSE) method is applied to hot inviscid Mach 0.7 and Mach 2 axisymmetric jets.
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Modified rational Legendre approach to laminar viscous flow over a semi-infinite flat plate
TL;DR: In this paper, a modified rational Legendre tau method is proposed to solve the classical Blasius' equation, which is a third order nonlinear ordinary differential equation in the problem of the two-dimensional laminar viscous flow over a semi-infinite flat plane.
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Shear stabilization of miscible displacement processes in porous media
A. Rogerson,Eckart Meiburg +1 more
TL;DR: In this article, the authors analyzed the interface region between two fluids of different densities and viscosities in a porous medium in which gravity is directed at various angles to the interface.
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.