Contents · 8 Sections
Overview
Mesh independence is the minimum standard before quoting a CFD result. This note documents a structured refinement study for the two-dimensional flow past a circular cylinder at a Reynolds number of 200, a well-known unsteady benchmark [1]. The goal is to find the coarsest mesh that still predicts the Strouhal number and mean drag coefficient within 2% of an accepted reference.
All data in this note is synthetic and marked as Demo. The procedure, file structure and reporting format follow real practice.
Problem definition
A circular cylinder of diameter D is placed in a rectangular domain. The inlet velocity U is chosen so that Re = UD/ν = 200. At this Reynolds number the flow is laminar, two-dimensional and periodic, with a regular von Kármán street.
- Domain: [-8D, 16D] × [-8D, 8D]
- Boundary conditions: uniform inlet, zero-gradient outlet, slip top/bottom, no-slip cylinder
- Monitored quantities: mean drag coefficient C̄D, rms lift coefficient C′L,rms, Strouhal number St
Mesh family
Four O-grid type meshes are generated with geometric progression in the wake and near-wall refinement. Cell counts are increased by roughly a factor of two between levels.
| Mesh | Cells | y+ max | Wake cells | Wake expansion ratio |
|---|---|---|---|---|
| M0 (coarse) | 18,400 | 2.8 | 80 | 1.10 |
| M1 | 38,200 | 1.9 | 120 | 1.08 |
| M2 | 76,800 | 1.2 | 180 | 1.06 |
| M3 (fine) | 154,000 | 0.8 | 260 | 1.05 |
Solver settings
The simulations use the OpenFOAM pimpleFoam solver with a second-order backward scheme for time and linear-upwind convection. A fixed time step of Δt = 0.005 s gives a maximum Courant number below 1.0 on the finest mesh.
solvers
{
p
{
solver GAMG;
tolerance 1e-7;
relTol 0.01;
}
U
{
solver smoothSolver;
smoother symGaussSeidel;
tolerance 1e-8;
relTol 0.1;
}
}
Results
Each case is run until the lift signal reaches a statistically periodic state. The reported values are averaged over at least twenty shedding cycles after transients have decayed.
| Mesh | C̄D | C′L,rms | St | ΔSt vs ref (%) |
|---|---|---|---|---|
| M0 | 1.412 | 0.582 | 0.196 | +1.55 |
| M1 | 1.389 | 0.601 | 0.193 | +0.00 |
| M2 | 1.384 | 0.608 | 0.193 | +0.00 |
| M3 | 1.383 | 0.610 | 0.193 | +0.00 |
Discussion
M1 already reproduces the reference Strouhal number within the 2% tolerance. Drag and lift coefficients change by less than 1% between M1 and M3, suggesting that M1 is the practical mesh-independent level for the quantities of interest.
M0 over-predicts the shedding frequency and under-predicts the rms lift, which is consistent with insufficient wake resolution. M2 and M3 agree closely, so further refinement only adds cost without changing engineering conclusions.
Dataset & reproduction
The case files are organized so the study can be reproduced from a clean OpenFOAM installation. The repository contains the mesh generation script, four case directories, a runner that executes all meshes in sequence, and a Python script that extracts the integrated quantities.