Sphere
Example simulation of a sphere
The analytical solution for the potential flow around a sphere of radius
R=1R=1
m and a uniform flow of
Vref=1|\mathbf{V}_{ref}|=1
m/s is known. The perturbation (or doublet) potential is given by:
ϕ=Vrefcos(θ)R32r2,\phi=|\mathbf{V}_{ref}|cos(\theta)\frac{R^3}{2r^2}\text{,}
where
ϕ\phi
is the perturbation (or doublet) potential,
RR
is the radius of the sphere,
rr
is the distance from the sphere centre to any point of interest on its surface,
Vref|\mathbf{V}_{ref}|
is the freestream velocity magnitude, and
θ\theta
is the angle between the
xx
-axis and the projection of
rr
on the
xzx-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.

sphere.zip
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