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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Direct Trajectory Optimization Using a Variable Low-Order Adaptive Pseudospectral Method
TL;DR: In this paper, a variable-order adaptive pseudospectral method is presented for solving optimal control problems, which adjusts both themesh spacing and the degree of the polynomial on each mesh interval until a specified error tolerance is satisfied.
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Large eddy simulation of turbulence‐driven secondary flow in a square duct
TL;DR: In this article, the authors used the large eddy simulation (LES) technique to simulate turbulent flow in a straight duct of square cross section and showed that both the Reynolds normal and shear stresses equally contribute to the production of mean streamwise vorticity.
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Some current CFD issues relevant to the incompressible Navier-Stokes equations
TL;DR: The goals of this paper are to carefully define a particular class of well-set incompressible Navier-Stokes problems in the continuum (partial differential equation/PDE) setting and to discuss some relevant and sometimes poorly understood issues related to these well-posed PDE problems, both in the continuity world and in its computer counterpart.
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Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity: Method and tests
TL;DR: In this paper, a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the precoalescing stage is presented, where a hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational.
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Numerical Simulation of Low Mach Number Reactive Flows
TL;DR: In this paper, a new formulation for numerical solution of low Mach number compressible flow problems is presented and analyzed, where the thermal part (energy and species equations) is solved implicitly and decoupled from the momentum equation, whereas the hydrodynamic part (momentum-continuity) is advanced in time using a high order splitting approach.
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.