From 21638b148197f1208508e737a6a2b62176b28ffa Mon Sep 17 00:00:00 2001 From: Niklas Fehn Date: Fri, 17 Apr 2020 18:12:52 +0200 Subject: [PATCH] improve documentation of step-35 --- examples/step-35/doc/results.dox | 42 ++++++++++++++------------------ 1 file changed, 18 insertions(+), 24 deletions(-) diff --git a/examples/step-35/doc/results.dox b/examples/step-35/doc/results.dox index 9ad0f9436b..5cb50255c0 100644 --- a/examples/step-35/doc/results.dox +++ b/examples/step-35/doc/results.dox @@ -107,35 +107,27 @@ yields the following images at times $t=20,40$: -What does look right is that with the higher Reynolds number, the flow -is much more unorganized, swaying between the bottom and top boundary -of the domain. On the other hand, the vorticity can't be right: it -oscillates rapidly, not something we would expect for a Reynolds -number that is still only moderate and that would not produce -small scale dynamics. The riddle is easily solved, -however, by looking at a zoom at the region behind the obstacle, and +For this larger Reynolds number, we observe unphysical oscillations, especially +for the vorticity. The discretization scheme has now difficulties in correctly +resolving the flow, which should still be laminar and well-organized. +These phenomena are typical of discretization schemes that lack robustness +in under-resolved scenarios, where under-resolved means that the Reynolds +number computed with the mesh size instead of the physical dimensions of +the geometry is large. We look at a zoom at the region behind the obstacle, and the mesh size we have there: - -It is clear here that the flow is still reasonably well resolved in -the immediate wake of the obstacle, where the mesh is relatively fine, -but that the problem appears where the mesh becomes too coarse. That -shouldn't surprise us: if we increase the Reynolds number, the scales -on which we expect flow variation decrease and we will have to have a -finer mesh. + -A rerun with one more mesh refinement set in the parameter file -confirms that results look much more sensible now: +We can easily test our hypothesis by re-running the simulation with one more +mesh refinement set in the parameter file: -Here, the zone where the mesh becomes coarser is immediately -downstream of the big red blob at the bottom of the wake behind the -obstacle. While there are still quite visible oscillations beyond that -point, it is clear that mesh refinement has already significantly -helped, and we can expect that further refining the mesh will suppress -the remaining oscillations as well. +Indeed, the vorticity field now looks much smoother. While we can expect that +further refining the mesh will suppress the remaining oscillations as well, +one should take measures to obtain a robust scheme in the limit of coarse +resolutions, as described below. @@ -152,8 +144,10 @@ This program can be extended in the following directions: practice shows that they perform very well.
  • High Reynolds %numbers: As we can see from the results, increasing the Reynolds number changes significantly - the behavior of the flow. Using well-known stabilization techniques we could be able to - compute the flow in this, or many other problems, when the Reynolds number is very large. + the behavior of the discretization scheme. Using well-known stabilization techniques we could be able to + compute the flow in this, or many other problems, when the Reynolds number is very large and where computational + costs demand spatial resolutions for which the flow is only marginally resolved, especially for 3D turbulent + flows.
  • Variable density incompressible flows: There are projection-like methods for the case of incompressible flows with variable density. Such flows play a role if fluids of different -- 2.39.5