Incompressible flow

Compressibility

Turbulence

Reynolds number

Applied mathematics

Vortex

Pressure-correction method

Grid

Thermodynamics

Physics

Finite element method

Mesh generation

Stream function

Navier–Stokes equations

Mathematics

Flow (mathematics)

Vorticity

Multigrid method

Mathematical analysis

Geometry

Polygon mesh

Partial differential equation

Mechanics

Journal of Computational Physics

The vorticity-stream function formulation of the two-dimensional incompressible Navier-Stokes equations is used to study the effectiveness of the coupled strongly implicit multigrid (CSI-MG) method in the determination of high-Re fine-mesh flow solutions. The driven flow in a square cavity is used as the model problem. Solutions are obtained for configurations with Reynolds number as high as 10,000 and meshes consisting of as many as 257 × 257 points. For Re = 1000, the (129 × 129) grid solution required 1.5 minutes of CPU time on the AMDAHL 470 V/6 computer. Because of the appearance of one or more secondary vortices in the flow field, uniform mesh refinement was preferred to the use of one-dimensional grid-clustering coordinate transformations.

High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method