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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A spectral/finite difference method for simulating large deformations of heterogeneous, viscoelastic materials
TL;DR: In this paper, a numerical algorithm is presented that simulates large deformations of heterogeneous, viscoelastic materials in two dimensions, based on a spectral/finite difference method and uses the Eulerian formulation including objective derivatives of the stress tensor in the rheological equations.
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A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow
Weinan E,Chi-Wang Shu +1 more
TL;DR: In this article, high-order essentially non-oscillatory (ENO) schemes are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions.
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Solitary-wave solutions of the Benjamin equation
TL;DR: A constructive proof of the existence of these waves together with a proof of their stability is developed and Continuation methods are used to generate a scheme capable of numerically approximating these solitary waves.
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Discontinuous Galerkin methods for general-relativistic hydrodynamics: formulation and application to spherically symmetric spacetimes
David Radice,Luciano Rezzolla +1 more
TL;DR: In this article, the authors have developed the formalism necessary to employ the discontinuous-Galerkin approach in general-relativistic hydrodynamics, which is first presented in a general four-dimensional setting and then specialized to the case of spherical symmetry within a $3+1$ splitting of spacetime.
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Direct numerical simulation of autoignition in a non-premixed, turbulent medium
TL;DR: In this article, a pressure-based method was proposed to simulate autoignition in an initially non-premixed medium under isotropic, homogeneous, and decaying turbulence.
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.