Spectral Methods for Incompressible Viscous Flow

By R. Peyret. 2002

838 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Fluid Flow and Transfer Processes

View Paper: https://www.semanticscholar.org/paper/f05014c8cbce899a80cc32e850bee72497b84d57

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In Applied Mathematics

In Computational Mechanics

In Fluid Flow and Transfer Processes

Citations in the corpus

On two-dimensional temporal modes in spatially evolving open flows: the flat-plate boundary layer (2005, methodology): “Since the use of Chebyshev polynomials provides the most efficient expansion of regular functions in terms of polynomials (Peyret 2002), we have considered an interpolation of the basic flow state and its derivatives on a Chebyshev-collocation grid in both space variables, in order to solve the stab”
On the relevance of subcritical hydrodynamic turbulence to accretion disk transport (2005, background): “Focusing for the time being on purely streamwise-independent perturbations, instability with respect to local perturbations follows when (Pedley 1969; Leblanc & Cambon 1997; Sipp & Jacquin 2000)”
A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems (2007, background): “These integrals can be determined by using recurrence relations [23] ∫ T0(x)dx = T1(x) (32) ∫ T1(x)dx = 1 4 [T0(x) + T2(x)] (33) ∫ Tk(x)dx = 1 2 [ Tk+1(x) (k + 1) − Tk−1(x) (k − 1) ] , k > 1 (34)”
A novel operational matrix method based on shifted Legendre polynomials for solving second-order boundary value problems involving singular, singularly perturbed and Bratu-type equations (2015, methodology): “Spectral methods (see, for instance [1–6]) are one of the principal methods of discretization for the numerical solution of differential equations.”
Spectral methods for hyperbolic problems (2001, methodology): “The application that is perhaps most responsible for the widespread use of spectral methods is the incompressible Navier-Stokes equations [8, 11, 52].”
A pseudospectral method of solution of Fisher's equation (2006, methodology): “Spectral methods have long been known to provide very accurate and rapidly convergent solutions of partial differential equations with smooth solutions [9,12,40].”
Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term (2004, methodology): “Liu / Journal of Computational Physics 199 (2004) 221–259 which can be solved efficiently using the matrix-diagonalization procedure [11,28].”
A Jacobi–Gauss collocation method for solving nonlinear Lane–Emden type equations (2012, methodology): “Spectral methods (see, for instance [7,17,24,27]) are one of the principal methods of discretization for the numerical solution of differential equations.”