> For the complete documentation index, see [llms.txt](https://docs.aviumtechnologies.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.aviumtechnologies.com/sphere.md).
# Sphere
The analytical solution for the potential flow around a sphere of radius $$R=1$$m and a uniform flow of $$|\mathbf{V}\_{ref}|=1$$ m/s is known. The perturbation (or doublet) potential is given by:
$$
\phi=|\mathbf{V}\_{ref}|cos(\theta)\frac{R^3}{2r^2}\text{,}
$$
where $$\phi$$ is the perturbation (or doublet) potential, $$R$$ is the radius of the sphere, $$r$$is the distance from the sphere centre to any point of interest on its surface, $$|\mathbf{V}\_{ref}|$$is the freestream velocity magnitude, and $$\theta$$is the angle between the $$x$$-axis and the projection of $$r$$on the $$x-z$$plane. An unstructured mesh of 532 elements is used. The image below shows the sphere pressure coefficient.
The images below compare the perturbation potential, the total potential, and the pressure coefficient with the analytical solution.
Good agreement between the simulation and the analytical solution is observed.
## Files
{% file src="/files/-MgbFgz2niNK6rIJuiBs" %}
## References