From 584d95bf216c8a082df58f23342c565b1fa69bef Mon Sep 17 00:00:00 2001 From: bangerth Date: Sat, 20 Sep 2008 03:01:34 +0000 Subject: [PATCH] Describe the testcase. git-svn-id: https://svn.dealii.org/trunk@16869 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-31/doc/intro.dox | 24 ++++++++++++++++++++++++ 1 file changed, 24 insertions(+) diff --git a/deal.II/examples/step-31/doc/intro.dox b/deal.II/examples/step-31/doc/intro.dox index 33ce876a6f..2efef78757 100644 --- a/deal.II/examples/step-31/doc/intro.dox +++ b/deal.II/examples/step-31/doc/intro.dox @@ -912,3 +912,27 @@ operations are relevant for the overall run time: In essence this means that all bottlenecks apart from the algebraic multigrid have been removed. + + + +

The testcase

+ +The case we want to solve here is as follows: we solve the Boussinesq +equations described above with $\kappa=1, \eta=1, \mathrm{Ra}=10$. On the +boundary, we will require no-normal flux for the velocity +($\mathrm{n}\cdot\mathrm{u}=0$) and for the temperature +($\mathrm{n}\cdot\nabla T=0$). No boundary conditions are required for the +pressure under these conditions. Initial conditions are only necessary for the +temperature field, and we choose it to be constant zero. + +The evolution of the problem is then entirely driven by the right hand side +$\gamma(\mathrm{x},t)$ of the temperature equation, i.e. by heat sources and +sinks. Here, we choose a setup invented in advance of a Christmas lecture: +real candles are of course prohibited in U.S. class rooms, but virtual ones +are allowed. We therefore choose three spherical heat sources unequally spaced +close to the bottom of the domain, imitating three candles. The fluid located +at these sources, initially at rest, is then heated up and as the temperature +rises gains buoyancy, rising up; more fluid is dragged up and through the +sources, leading to three hote plumes that rise up until they are captured by +the recirculation of fluid that sinks down on the outside, replacing the air +that rises due to heating. -- 2.39.5