Recent developments in the pure streamfunction formulation of the Navier-Stokes system

DOI10.1007/s10915-010-9374-1zbMath1203.76045OpenAlexW2034341896MaRDI QIDQ618625

Jean-Pierre Croisille, Matania Ben-Artzi, Dalia Fishelov

Publication date: 16 January 2011

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-010-9374-1

zbMATH Keywords

Navier-Stokes equationsvorticitynumerical algorithmstreamfunction formulationcompact schemes

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Finite element methods applied to problems in fluid mechanics (76M10) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (8)

A \(C^1\) virtual element method for the stationary quasi-geostrophic equations of the ocean ⋮ Recent advances in the study of a fourth-order compact scheme for the one-dimensional biharmonic equation ⋮ A high-order compact scheme for the pure streamfunction (vector potential) formulation of the 3D steady incompressible Navier-Stokes equations ⋮ A parallel high-order compact scheme for the pure streamfunction formulation of the 3D unsteady incompressible Navier-Stokes equation ⋮ A finite element discretization of the streamfunction formulation of the stationary quasi-geostrophic equations of the Ocean ⋮ Vorticity and stream function formulations for the 2D Navier-Stokes equations in a bounded domain ⋮ Enriched numerical scheme for singularly perturbed barotropic quasi-geostrophic equations ⋮ Implementation of Neumann boundary condition with influence matrix method for viscous annular flow using pseudospectral collocation

Cites Work

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• The stability of numerical boundary treatments for compact high-order finite-difference schemes
• A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations
• High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
• Essentially compact schemes for unsteady viscous incompressible flows
• Uncoupled finite element solution of biharmonic problems for vector potentials
• A Compact Difference Scheme for the Biharmonic Equation in Planar Irregular Domains
• A Fast Direct Solver for the Biharmonic Problem in a Rectangular Grid
• Convergence of a Compact Scheme for the Pure Streamfunction Formulation of the Unsteady Navier–Stokes System

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