Stokes eigenmodes in square domain and the stream function-vorticity correlation

DOI10.1016/j.jcp.2004.03.017zbMath1115.76319OpenAlexW2052803460MaRDI QIDQ1887745

Gérard Labrosse, Emmanuel Leriche

Publication date: 22 November 2004

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2004.03.017

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stokes and related (Oseen, etc.) flows (76D07) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items

Vector potential-vorticity relationship for the Stokes flows: Application to the Stokes eigenmodes in 2D/3D closed domain ⋮ Spectrally accurate Stokes eigen-modes on isosceles triangles ⋮ Anelastic Stokes eigenmodes in infinite channel ⋮ Buckling of a growing tissue and the emergence of two-dimensional patterns ⋮ Stokes eigenmodes in cubic domain: primitive variable and lattice Boltzmann formulations ⋮ Final states of decaying 2D turbulence in bounded domains: Influence of the geometry ⋮ Explicit lower bounds for Stokes eigenvalue problems by using nonconforming finite elements ⋮ A boundary integral equation approach to computing eigenvalues of the Stokes operator ⋮ Stokes eigenmodes on two-dimensional regular polygons ⋮ High performance computing for partial differential equations ⋮ Are there localized eddies in the trihedral corners of the Stokes eigenmodes in cubical cavity? ⋮ Traveling-waves consistent with turbulence-driven secondary flow in a square duct ⋮ Fundamental Stokes eigenmodes in the square: Which expansion is more accurate, Chebyshev or Reid-Harris? ⋮ A multilevel correction method for Stokes eigenvalue problems and its applications ⋮ The piecewise-linear finite volume scheme: The best known lowest-order preconditioner for the \(\frac{d^2}{dx^2}\) Chebyshev spectral operator

Uses Software

• Matlab
• ARPACK

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the eigenvalues of second-order spectral differentiation operators
• Boundary conditions for incompressible flows
• The free surface on a simple fluid between cylinders undergoing torsional oscillations. III: Oscillating planes
• Generalized Stokes eigenfunctions: A new trial basis for the solution of incompressible Navier-Stokes equations
• Creeping flow analyses of free surface cavity flows
• Fundamental Stokes eigenmodes in the square: Which expansion is more accurate, Chebyshev or Reid-Harris?
• High precision solutions of two fourth order eigenvalue problems
• Spectral method solution of the Stokes equations on nonstaggered grids
• High-Order Direct Stokes Solvers with or Without Temporal Splitting: Numerical Investigations of Their Comparative Properties
• A Legendre Spectral Galerkin Method for the Biharmonic Dirichlet Problem
• A numerical investigation of the solution of a class of fourth–order eigenvalue problems
• On steady laminar flow with closed streamlines at large Reynolds number
• Decaying two-dimensional turbulence in square containers with no-slip or stress-free boundaries
• The eddy structure in Stokes flow in a cavity
• Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
• Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials
• Timely Communication: Efficient Algorithms for Solving a Fourth-Order Equation with the Spectral-Galerkin Method
• ARPACK Users' Guide
• A Legendre Spectral Collocation Method for the Biharmonic Dirichlet Problem
• High-Order Methods for Incompressible Fluid Flow
• Viscous and resistive eddies near a sharp corner
• Decaying quasi-two-dimensional viscous flow on a square domain