A pseudospectral method for solution of the three-dimensional incompressible Navier-Stoke equations
type: Item
instance of: scholarly article
title: A pseudospectral method for solution of the three-dimensional incompressible Navier-Stoke equations
zbMATH Open document ID: 0658.76027
DOI: 10.1016/0021-9991(87)90190-2
author: Richard S. Hirsh
author: T. D. Taylor
author: Hwar-Ching Ku
published in: Journal of Computational Physics
publication date: 1987-01-01T00:00:00Z
review text: A new collocation spectral method is presented for solving the three- dimensional incompressible Navier-Stokes equations in primitive variables for nonperiodic boundary conditions. The functions are expanded in Chebyshev polynomials, the equations are collocated at the Chebyshev points, and Chorin's splitting method is used for the time discretization. For the resulting pressure Poisson equation a direct fast solver is proposed which is based on eigenfunction decompositions. This greatly reduces the computer storage requirments for solving the linear systems. The method is tested on the two- and three-dimensional cavity flow problem.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 65M99
Mathematics Subject Classification ID: 65N35
zbMATH DE Number: 4076815
zbMATH Keywords: Chebyshev pseudospectral technique
zbMATH Keywords: three-dimensional Navier-Stokes equations
zbMATH Keywords: collocation spectral method
zbMATH Keywords: three-dimensional incompressible Navier-Stokes equations
zbMATH Keywords: nonperiodic boundary conditions
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: Chorin's splitting method
zbMATH Keywords: Poisson equation
zbMATH Keywords: three- dimensional cavity flow problem
reviewed by: Walter Zulehner
MaRDI profile type: Publication
full work available at URL: 0021-9991(87)90190-2
OpenAlex ID: W1992002280
cites work: Application of a fractional-step method to incompressible Navier-Stokes equations
cites work: A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows
cites work: Numerical simulation of three-dimensional flow in a cavity
cites work: Transition to turbulence in plane Poiseuille and plane Couette flow
cites work: Pressure and time treatment for Chebyshev spectral solution of a Stokes problem
cites work: On the numerical solution of time-dependent viscous incompressible fluid flows involving solid boundaries
cites work: Numerical Solution of the Navier-Stokes Equations
cites work: The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
cites work: Chebyshev 3-D spectral and 2-D pseudospectral solvers for the Helmholtz equation
cites work: Accurate solution of three-dimensional Poisson's equation in cylindrical coordinate by expansion in Chebyshev polynomials
cites work: Spectral methods for problems in complex geometries
cites work: Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning
cites work: Spectral multigrid methods for elliptic equations
cites work: Chebyshev expansion methods for the solution of the extended Graetz problem
cites work: High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
cites work: Spectral multigrid methods with applications to transonic potential flow
cites work: Q4199478
description: scientific article; zbMATH DE number 4076815