A spectral solver for the Navier-Stokes equations in the velocity-vorticity formulation for flows with two nonperiodic directions
type: Item
instance of: scholarly article
title: A spectral solver for the Navier-Stokes equations in the velocity-vorticity formulation for flows with two nonperiodic directions
zbMATH Open document ID: 0904.76058
published in: Journal of Computational Physics
publication date: 1998-12-28T00:00:00Z
review text: A novel pseudospectral scheme for the Navier-Stokes equations with two nonperiodic directions is proposed. An influence matrix technique is employed to elicit the a priori lacking boundary conditions for the vorticity. The spatial discretization is based on a two-dimensional Chebyshev expansion on a nonstaggered grid of collocation points. The time marching scheme is Adams-Bashforth for the advective term and Crank-Nicholson for the viscous term. Divergence-free flow fields are achieved within machine accuracy.
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 65M70
zbMATH DE Number: 1100748
zbMATH Keywords: pseudospectral scheme
zbMATH Keywords: influence matrix technique
zbMATH Keywords: Chebyshev expansion
zbMATH Keywords: time marching scheme
zbMATH Keywords: nonstaggered grid
author: Herman J. H. Clercx
reviewed by: Wilhelm Heinrichs
MaRDI profile type: Publication
full work available at URL: jcph.1997.5799
OpenAlex ID: W2062760946
Wikidata QID: Q114873760
cites work: Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations
cites work: Finite-difference methods for calculating steady incompressible flows in three dimensions
cites work: A numerical study of the two-dimensional Navier-Stokes equations in vorticity-velocity variables
cites work: The numerical solution of the Navier-Stokes equations for 3-dimensional, unsteady, incompressible flows by compact schemes
cites work: A multigrid solver for the vorticity‐velocity Navier‐Stokes equations
cites work: A numerical method for the vorticity-velocity Navier-Stokes equations in two and three dimensions
cites work: Vorticity-velocity formulation for high Re flows
cites work: A vorticity-velocity method for the numerical solution of 3D incompressible flows
cites work: Finite element solution of the 3D compressible Navier-Stokes equations by a velocity-vorticity method
cites work: Resolution of the 2D Navier-Stokes equations in velocity-vorticity form by means of an influence matrix technique
cites work: Numerical solution of the incompressible Navier-Stokes equations
cites work: A divergence-free Chebyshev collocation procedure for incompressible flows with two non-periodic directions
cites work: On the advantages of the vorticity-velocity formulation of the equations of fluid dynamics
cites work: Numerical method for unsteady 3D Navier-Stokes equations in velocity-vorticity form
cites work: Application of vorticity integral conditioning to Chebyshev pseudospectral formulation for the Navier-Stokes equations
cites work: Q3776818
cites work: Numerical Methods for the Simulation of Turbulence
cites work: The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
cites work: Divergence-free velocity fields in nonperiodic geometries
cites work: Q3914616
cites work: Simulation of Taylor-Couette flow. Part 1. Numerical methods and comparison with experiment
cites work: Computation of natural convection in two-dimensional cavities with Chebyshev polynomials
cites work: A Chebyshev collocation algorithm for 2D non-Boussinesq convection
cites work: Incompressibility and no-slip boundaries in the Chebyshev-tau approximation: Correction to Kleiser and Schumann's influence-matrix solution
cites work: High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
cites work: Chebyshev collocation solutions of the Navier-Stokes equations using multi-domain decomposition and finite element preconditioning
cites work: Hopf bifurcation of the unsteady regularized driven cavity flow
cites work: The treatment of spurious pressure modes in spectral incompressible flow calculations
cites work: A steepest gradient method for optimum structural design
cites work: Accurate solutions to the square thermally driven cavity at high Rayleigh number
cites work: A three-dimensional pseudo-spectral algorithm for the computaion of convection in a rotating annulus
DOI: 10.1006/JCPH.1997.5799
Recommended article: A spectral solver for the Navier–Stokes equations in the velocity–vorticity formulation
Recommended article: Q4801490
Recommended article: Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions
Recommended article: Spectral discretization of the axisymmetric vorticity, velocity and pressure formulation of the Navier-Stokes problem
Recommended article: Spectral discretization of the vorticity, velocity and pressure formulation of the Navier-Stokes equations
Recommended article: Spectral discretization of time-dependent vorticity-velocity-pressure formulation of the Navier-Stokes equations
Recommended article: Spectral-finite element method for solving two-dimensional vorticity equations
Recommended article: Q3835164
Recommended article: Q3821760
Recommended article: Q3735268
description: scientific article; zbMATH DE number 1100748