From: Wolfgang Bangerth Date: Tue, 26 May 2020 20:20:44 +0000 (-0600) Subject: Hook in videos of second-order results for step-69. X-Git-Tag: v9.3.0-rc1~1549^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=164d194f25e252a8e366001c84d351df2bac2792;p=dealii.git Hook in videos of second-order results for step-69. --- diff --git a/examples/step-69/doc/results.dox b/examples/step-69/doc/results.dox index 3123f6987a..995b4f290a 100644 --- a/examples/step-69/doc/results.dox +++ b/examples/step-69/doc/results.dox @@ -151,3 +151,57 @@ And with the following result: That's substantially better, although of course at the price of having run the code for roughly 2 hours on 16 cores. + + + + +

Possibilities for extensions

+ +The program showcased here is really only first-order accurate, as +discussed above. The pictures above illustrate how much diffusion that +introduces and how far the solution is from one that actually resolves +the features we care about. + +This can be fixed, but it would exceed what a *tutorial* is +about. Nevertheless, it is worth showing what one can achieve by +adding a second-order scheme. For example, here is a video that shows +(with a different color scheme) a 2d simulation that corresponds to +the cases shown above: + +@htmlonly +

+ +

+@endhtmlonly + +This simulation was done with 38 million degrees of freedom +(continuous $Q_1$ finite elements) per component of the solution +vector. The exquisite detail of the solution is remarkable for these +kinds of simulations, including in the sub-sonic region behind the +obstacle. + +One can also with relative ease further extend this to the 3d case: + +@htmlonly +

+ +

+@endhtmlonly + +Solving this becomes expensive, however: The simulation was done with +1,817 million degrees of freedom (continuous $Q_1$ finite elements) +per component (for a total of 9.09 billion spatial degrees of freedom) +and ran on 30,720 MPI ranks. The code achieved an average througput of +969M grid points per second (0.04M gridpoints per second per CPU). The +front and back wall show a "Schlieren plot": the magnitude of the +gradient of the density on an exponential scale from white (low) to +black (high). All other cutplanes and the surface of the obstacle show +the magnitude of the vorticity on a white (low) - yellow (medium) - +red (high) scale. (The scales of the individual cutplanes have been +adjusted for a nicer visualization.)