<i>This program was contributed by Luca Heltai (thanks to Michael
Gratton for pointing out what the exact solution should have been in
-the threedimensional case). </i>
+the three dimensional case). </i>
<a name="Intro"></a>
mesh.
For a sphere of radius $a$ translating at a velocity of $U$ in the $x$ direction, the potential reads
-\[
+\[
\phi = -\frac{1}{2}U \left(\frac{a}{r}\right)3 r \cos\theta
\] see, e.g. J.N. Newman, \emph{Marine Hydrodynamics}, 1977,
pp. 127. For unit speed and radius, and restricting $(x,y,z)$ to lie
-on the surface of the sphere,
+on the surface of the sphere,
\[ \phi = -x/2.\] In the test problem,
the flow is $(1,1,1)$, so the appropriate exact solution on the
surface of the sphere is the superposition of the above solution with
the analogous solution along the $y$ and $z$ axes, or \[ \phi =
-\frac{1}{2}(x + y + z) \]
\ No newline at end of file
+\frac{1}{2}(x + y + z) \]