A semi-Lagrangian method for turbulence simulations using mixed spectral discretizations
type: Item
instance of: scholarly article
title: A semi-Lagrangian method for turbulence simulations using mixed spectral discretizations
zbMATH Open document ID: 1028.76020
DOI: 10.1023/A:1015122714039
author: Jin Xu
author: Dongbin Xiu
author: George Em Karniadakis
published in: Journal of Scientific Computing
publication date: 2002-08-20T00:00:00Z
review text: The paper describes a spectral semi-Lagrangian method for solving three-dimensional incompressible Navier-Stokes equations. A turbulent channel flow is considered with two homogeneous directions where periodic boundary conditions are imposed, and with one inhomogeneous direction where no-slip conditions are applied. The corresponding space discretization uses Fourier collocation in two homogeneous directions and a spectral element technique with Jacobi polynomials in the inhomogeneous direction. The time-discretization is second-order accurate for both Navier-Stokes equations in Lagrangian form and for the characteristic equations. For the latter an explicit backward integration is used, and the interpolation of velocity at departure points is performed by direct summation of Fourier expansions, which is computationally expensive. The spectral convergence of the method in space and the non-monotonic behaviour of temporal error are studied for an exact solution of three-dimensional Navier-Stokes equations. Finally, direct numerical simulations of a turbulent channel flow are presented, and the results of semi-Lagrangian method are compared with those obtained by an Eulerian scheme.
reviewed by: Kai Schneider
Mathematics Subject Classification ID: 76F65
Mathematics Subject Classification ID: 76M22
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 1784264
zbMATH Keywords: direct numerical simulation
zbMATH Keywords: spectral elements
zbMATH Keywords: semi-Lagrangian schemes
zbMATH Keywords: spectral semi-Lagrangian method
zbMATH Keywords: three-dimensional incompressible Navier-Stokes equations
zbMATH Keywords: turbulent channel flow
zbMATH Keywords: homogeneous directions
zbMATH Keywords: inhomogeneous direction
zbMATH Keywords: Fourier collocation
zbMATH Keywords: spectral element technique
zbMATH Keywords: Jacobi polynomials
zbMATH Keywords: explicit backward integration
zbMATH Keywords: direct summation of Fourier expansions
zbMATH Keywords: spectral convergence
zbMATH Keywords: temporal error
zbMATH Keywords: direct numerical simulations
MaRDI profile type: Publication
full work available at URL: a:1015122714039
OpenAlex ID: W1487739288
description: scientific article; zbMATH DE number 1784264