From 1764a83aeecf6bffb1f779f08e41ad524c2794b9 Mon Sep 17 00:00:00 2001 From: bangerth Date: Fri, 1 Feb 2013 01:00:10 +0000 Subject: [PATCH] Minor typo. git-svn-id: https://svn.dealii.org/trunk@28208 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-34/doc/intro.dox | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/deal.II/examples/step-34/doc/intro.dox b/deal.II/examples/step-34/doc/intro.dox index 420350d0b6..5b3b847f9b 100644 --- a/deal.II/examples/step-34/doc/intro.dox +++ b/deal.II/examples/step-34/doc/intro.dox @@ -2,7 +2,7 @@ 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). +the three dimensional case). @@ -660,14 +660,14 @@ that respects the continuous geometry behind the discrete initial 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) \] -- 2.39.5