Spectral Methods In Fluid Dynamics
Annual Review of Fluid MechanicsPublished 1 January 1987
M. Yousuff Hussaini
Citations2,365
SJR quartileQ1
SJR score8.26
SNIP11.38
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
Chapters 4 to 8 for the algorithms and Chapters 9 to 12 for the analysis.Nevertheless, and despite the particular research interests of
Keywords
EngineeringChemical Engineering
Journal of Computational PhysicsA spectral element method for fluid dynamics: Laminar flow in a channel expansion
2,264 Citations1984Anthony T. Patera
Annual Review of Fluid MechanicsNumerical Simulation of Turbulent Flows
901 Citations1984R S Rogallo, Parviz Moin
Journal of Computational PhysicsSpectral methods for problems in complex geometries
662 Citations1980Steven A. Orszag
It is shown that the work required to solve the full matrix equations resulting from spectral approximations to nonconstant coefficient boundary-value problems in complex geometries exceeds that of solving the lowest-order finite-difference approximation to the same problem by only O(N log N).
Stanford Univ. ReportImproved turbulence models based on large eddy simulation of homogeneous, incompressible turbulent flows
412 Citations1983J. Bardino, Joel H. Ferziger +1 more
AIAA JournalDirect numerical simulations of a reacting mixing layer with chemical heat release
256 Citations1986Patrick McMurtry, Wen-Huei Jou +2 more
Journal of Computational PhysicsThe accurate solution of poisson's equation by expansion in chebyshev polynomials
255 Citations1979Dale B. Haidvogel, Thomas A. Zang
Journal of Fluid MechanicsEffect of rotation on isotropic turbulence: computation and modelling
246 Citations1985J. Bardina, Joel H. Ferziger +1 more
Journal of Computational PhysicsSpectral methods using rational basis functions on an infinite interval
227 Citations1987John P. Boyd
Journal of Computational PhysicsDifferential eigenvalue problems in which the parameter appears nonlinearly
221 Citations1984Thomas J. Bridges, Philip J. Morris
The Physics of FluidsSecondary instability of plane channel flow to subharmonic three-dimensional disturbances
212 Citations1983Thorwald Herbert
Journal of Computational PhysicsA spectral numerical method for the Navier-Stokes equations with applications to Taylor-Couette flow
187 Citations1983Robert Moser, Parviz Moin +1 more
Journal of Computational PhysicsSelf-sorting mixed-radix fast Fourier transforms
171 Citations1983Clive Temperton
The implementation of the FFT on vector computers is described, and in the final section it is demonstrated how savings can be achieved in the case of two-dimensional transforms.
Journal of Fluid MechanicsThe structure of the vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields
169 Citations1986John Kim, Parviz Moin
Journal of Fluid MechanicsExperiments on a viscous fluid flow between concentric rotating spheres
160 Citations1976M. Wimmer
Journal of Computational PhysicsChebyshev 3-D spectral and 2-D pseudospectral solvers for the Helmholtz equation
155 Citations1984Pierre Haldenwang, G. Labrosse +2 more
Two Chebyshev solvers are presented for the linear Helmholtz equation, one a 3-D direct spectral solver based on a diagonalization technique and the other an iterative pseudospectral 2-D calculation with finite difference preconditioning.
Mathematics of ComputationThe Fourier method for nonsmooth initial data
139 Citations1978Andrew J. Majda, J. M. McDonough +1 more
The Physics of FluidsDirect numerical simulations of chemically reacting turbulent mixing layers
138 Citations1986James J. Riley, Ralph W. Metcalfe +1 more
Journal of Computational PhysicsA spectral collocation method for the Navier-Stokes equations
119 Citations1985Mujeeb R. Malik, T. A. Zang +1 more
SIAM Journal on Numerical AnalysisThe Spectrum of the Chebyshev Collocation Operator for the Heat Equation
111 Citations1983David Gottlieb, Liviu Lustman
Proceedings of the Royal Society of London A Mathematical and Physical SciencesNumerical experiments in boundary-layer stability
109 Citations1984A. A. Wray, M. Yousuff Hussaini
Journal of Computational PhysicsChebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning
107 Citations1985Michel Deville, E Mund
A new Chebyshev pseudospectral algorithm for second-order elliptic equations using finite element preconditioning is proposed and tested on various problems and the numerical results show that bilinear elements produce spectral accuracy with the minimum computational work.
Direct Numerical Simulation of Equilibrium Turbulent Boundary Layers
93 Citations1987Philippe R. Spalart, Anthony Leonard
Journal of Fluid MechanicsThe instability of oscillatory plane Poiseuille flow
78 Citations1982C. H. von Kerczek
AIAA JournalNumerical Study of Nonlinear Effects on Boundary-Layer Stability
61 Citations1977John W. Murdock
NASA Technical Reports Server (NASA)Direct numerical simulation of curved turbulent channel flow
60 Citations1984Robert Moser, Parviz Moin
Journal of Computational PhysicsDiscrete orthogonal function expansions for non-uniform grids using the fast fourier transform
59 Citations1984Alan Cain, Joel H. Ferziger +1 more
Spectral Methods for Discontinuous Problems
53 Citations1985Saul Abarbanel, David Gottlieb +1 more
Applied Mathematics and ComputationOn spectral multigrid methods for the time-dependent Navier-Stokes equations
49 Citations1986Thomas A. Zang, M. Yousuff Hussaini
A new splitting scheme is proposed for the numerical solution of the time-dependent incompressible Navier-Stokes equations by spectral methods using staggered grid, improved intermediate boundary conditions, and spectral multigrid techniques for the solution ofThe implicit equations.
Journal of Computational PhysicsComplex coordinate methods for hydrodynamic instabilities and Sturm-Liouville eigenproblems with an interior singularity
46 Citations1985John P. Boyd
Journal of Computational PhysicsSpectral multigrid methods with applications to transonic potential flow
43 Citations1985Craig L. Streett, Thomas A. Zang +1 more
Numerische MathematikSpectral methods for exterior elliptic problems
27 Citations1985Claudio Canuto, S. I. Hariharan +1 more
Journal of Computational PhysicsImproved spectral multigrid methods for periodic elliptic problems
27 Citations1985Achi Brandt, Scott R. Fulton +1 more
Several modifications are introduced, including a midpoint pseudospectral discretization which eliminates the need for filtering the highest Fourier mode and new relaxation schemes for isotropic and anisotropic problems.
Lecture notes in physicsNumerical simulation of boundary-layer transition
21 Citations2008Philippe R. Spalart
Journal of Computational PhysicsTechnical improvements for direct numerical simulation of homogeneous three-dimensional turbulence
21 Citations1983C. Basdevant
NASA Technical Reports Server (NASA)Spectral methods for inviscid, compressible flows
19 Citations1983M. Yousuff Hussaini, Manuel D. Salas +1 more
The spectral multigrid iterative methods are discussed with application to the transonic full potential equation and the key element is the shock fitting technique which is briefly explained.
NASA STI/Recon Technical Report NSimulation and modeling of homogeneous, compressed turbulence
19 Citations1985C. T. Wu, Joel H. Ferziger +1 more
Lecture notes in physicsMixed spectral/finite difference approximations for slightly viscous flows
17 Citations2008Thomas A. Zang, M. Yousuff Hussaini
IMA Journal of Numerical AnalysisPreconditioners for the Spectral Multigrid Method
17 Citations1986Timothy N. Phillips, Thomas A. Zang +1 more
A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made and new preconditionsing techniques based on higher order finite differences and on the spectral matrix itself are presented.
Journal of Computational PhysicsOn the boundary treatment in spectral methods for hyperbolic systems
17 Citations1987Claudio Canuto, Alfio Quarteroni
Lecture notes in physicsShock-fitted Euler solutions to shock-vortex interactions
16 Citations2008Manuel D. Salas, Thomas A. Zang +1 more
Numerical Methods in Laminar and Turbulent FlowPseudospectral calculation of shock turbulence interactions
12 Citations1983T. A. Zang, David A. Kopriva +1 more
Elsevier eBooksTemporal Discretization
7 Citations2015Jiří Blažek
This work focuses on explicit methods and presents Runge-Kutta and hybrid multistage schemes, and presents approaches for unsteady flows, in particular the dual time-stepping method.
Two-dimensional problems
7 Citations1993Sir Nevill Mott
Theory of Stability and Convergence for Spectral Methods
6 Citations1988Claudio Canuto, M. Yousuff Hussaini +2 more
American Institute of Aeronautics and Astronautics eBooksNumerical Simulation of Homogeneous Turbulence Submitted to Two Successive Plane Strains and Solid Body Rotation
3 Citations1985
Solution Techniques for Implicit Spectral Equations
3 Citations1988Claudio Canuto, M. Yousuff Hussaini +2 more
This work focuses on linear systems, assuming that non-linear ones are attacked by standard linearization techniques and is concerned with implicit equations.
Lecture notes in computational science and engineeringThe Spectral Element Method
3 Citations1997Daniele Funaro
This work analyzes the discretization of elliptic boundary-value problems defined in domains with a complicated shape, via a domain decomposition approach, and approximated solution is a patchwork of different algebraic polynomials defined in the subdomains.
AIAA JournalPseudospectral Solutions of One- and Two-Dimensional Inviscid Flows with Shock Waves
3 Citations1984Leonidas Sakell