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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Numerical simulation of dynamics of premixed flames: flame instability and vortex–flame interaction
TL;DR: In this article, three basic types of phenomena responsible for the intrinsic instability of premixed flames are examined, i.e., hydrodynamic, body-force and diffusive-thermal effects.
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Computational Aerodynamics for Aircraft Design
TL;DR: Some of the principal issues in the development of numerical methods for the prediction of flows over aircraft and their use in the design process include the choice of an appropriate mathematical model, the design of shock-capturing algorithms, and shape modifications to optimize the aerodynamic performance.
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Stagnation-point flow of upper-convected Maxwell fluids
TL;DR: In this paper, the velocity inside the boundary layer may exceed that outside the layer may just be an artifact of the rheological model used in previous studies (namely, the second-grade model).
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A fast method for fully nonlinear water-wave computations
Didier Clamond,John Grue +1 more
TL;DR: A fast computational method for fully nonlinear non-overturning water waves is derived in two and three dimensions and one iteration is found to be sufficient for practical computations, while maintaining high accuracy.
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Spectral Methods for Partial Differential Equations in Irregular Domains: The Spectral Smoothed Boundary Method
TL;DR: A numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by using a smoothing term to encode the boundary conditions into a modified equation that can be approached by standard spectral methods.
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.