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
More filters
Journal ArticleDOI
Computation of electromagnetic scattering with a non‐conforming discontinuous spectral element method
TL;DR: In this paper, a high-order quadrilateral discontinuous spectral element method (DSEM) is proposed to solve electromagnetic scattering problems by approximating Maxwell's equations in the time-domain with a highorder Quadrilateral Discriminative Spectral Element Method.
Journal ArticleDOI
The analysis and simulation of compressible turbulence
TL;DR: In this article, it is shown that even if the divergence of the initial velocity field is negligibly small, it can grow rapidly on a non-dimensional time scale which is the inverse of the fluctuating Mach number.
Journal ArticleDOI
Efficient Spectral-Galerkin Methods III: Polar and Cylindrical Geometries
TL;DR: Several extremely efficient and accurate spectral-Galerkin methods for second- and fourth-order equations in polar and cylindrical geometries based on appropriate variational formulations which incorporate naturally the pole condition(s).
Journal ArticleDOI
Sensitive dependence on initial conditions in transition to turbulence in pipe flow
Holger Faisst,Bruno Eckhardt +1 more
TL;DR: In this article, the authors show that the transition to turbulence is connected with the formation of a chaotic saddle in the phase space of the system and quantify a sensitive dependence on initial conditions and find in a statistical analysis that the distribution of turbulent lifetimes follows an exponential law.
Journal ArticleDOI
A new triangular and tetrahedral basis for high-order (hp) finite element methods
TL;DR: The foundations of a new hierarchical modal basis suitable for high-order (hp) finite element discretizations on unstructured meshes is described, based on a generalized tensor product of mixed-weight Jacobi polynomials.
References
More filters
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.