cylinder2dRe100

2D flow around a stationary cylinder (Re=100)

A circular cylinder of diameter $D=1.0$ is placed at the origin of a two-dimensional domain spanning $\left[ -15, 35 \right] \times \left[ -25, 25 \right]$. The initial velocity of the fluid in the domain is $\left( 1, 0 \right)$. Dirichlet conditions for the velocity are set on all boundaries (velocity set to $\left( 1, 0 \right)$), except at the outlet where the fluid is convected outside the domain in the $x$-direction at speed $1.0$. The Reynolds number (based on the freestream speed, the diameter of the circular cylinder, and the kinematic viscosity) is $100$.

The computational domain is discretized using an stretched Cartesian grid with $510 \times 298$ cells. The mesh is kept uniform in the sub-domain $\left[ -0.75, 0.75 \right] \times \left[ -0.75, 0.75 \right]$ and stretched to the external boundaries with a constant ratio; we use a ratio of $1.04$ in the $y$ direction, $1.03$ in the $x$ direction upstream the cylinder, and $1.01$ in the $x$ direction downstream the cylinder.

For this example, we run the simulation with the immersed-boundary projection method implemented in PetIBM for $20000$ time steps with a time increment of $0.01$, saving the numerical solution every $1000$ time steps.

⚠️

All commands displayed below assume you are in the directory containing the present README file.

Run the example

docker pull barbagroup/petibm:0.5.1-GPU-OpenMPI-xenial
nvidia-docker run --rm -it -v $(pwd):/data barbagroup/petibm:0.5.1-GPU-OpenMPI-xenial /data/run.sh

ℹ️

For reference, the simulation completed 20,000 time steps in about 25 minutes using

• 2 MPI processes (Intel(R) Core(TM) i7-3770 CPU @ 3.40GHz)
• 1 NVIDIA K40 GPU device

Post-processing

Activate your conda environment (see instructions):

conda activate petibm-examples

Plot the history of the force coefficients:

python scripts/plot_force_coefficients.py

The figure is saved as a PNG file (force_coefficients.png) in the sub-folder figures of the present simulation directory.

Figure: History of the force coefficients for the cylinder at Reynolds number $100$.

Plot the history of the force coefficients and compare with the IBPM solution:

python scripts/plot_force_coefficients_compare_ibpm.py

The figure is saved as a PNG file (force_coefficients_compare_ibpm.png) in the sub-folder figures of the present simulation directory.

Figure: History of the force coefficients for the cylinder at Reynolds number $100$.

Plot the surface pressure coefficient and compare with numerical data from Li et al. (2016):

python scripts/plot_pressure_coefficient.py

The figure is saved as a PNG file (pressure_coefficient.png) in the sub-folder figures of the present simulation directory.

Figure: Pressure coefficient interpolated along the surface of the cylinder for Reynolds number $100$. Comparison with the numerical data reported by Li et al. (2016).

Plot the surface pressure coefficient and compare with the IBPM solution and with numerical data from Li et al. (2016):

python scripts/plot_pressure_coefficient_compare_ibpm.py

The figure is saved as a PNG file (pressure_coefficient_compare_ibpm.png) in the sub-folder figures of the present simulation directory.

Figure: Pressure coefficient interpolated along the surface of the cylinder for Reynolds number $100$. Comparison with the numerical data reported by Li et al. (2016).

Plot the contours of the vorticity field after 20,000 time steps:

python scripts/plot_vorticity.py

The figure is saved as a PNG file (wz_0020000.png) in the sub-folder figures of the present simulation directory.

Figure: Contours of the vorticity field at Reynolds number $100$ (contours between $-3$ and $3$ with increments of $0.4$).

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References

• Li, R. Y., Xie, C. M., Huang, W. X., & Xu, C. X. (2016). An efficient immersed boundary projection method for flow over complex/moving boundaries. Computers & Fluids, 140, 122-135.