Hi Geordie and Hans-Joerg
Thanks for your file Geordie.
Just my 1 centime au Franc (the pages are in French!):
I did an exam for my students with this problem (comparisons with
Gill 66 analytical solution), solving it with FreeFem++ (a nice piece
of free software as well):
http://www.lmm.jussieu.fr/~lagree/COURS/ENSTA/web/CLib/thermiKVIT/
index.html
I put at the end of this page my current version of the modified
Boussinesq in a box:
http://www.lmm.jussieu.fr/~lagree/COURS/ENSTA/web/CLib/thermiKVIT/
KVITboussinesq/KVITboussinesq.gfs
@++
Le 25 mars 09 à 01:07, G. D. McBain a écrit :
> On Tue, Mar 24, 2009 at 05:24:53AM -0300, Hanjoerg Seybold wrote:
>> Hi Geordie,
>> I had a look at the thread, but i could only find the shell script
>> in the
>> attachment. I would be really interested how you solved the cavity
>> advection.
>> Thanks hj
>
> Hello. That's strange, isn't it, I see what you mean, if you just go
> to the URL I sent only the first of the four attachments is there, but
> if you click to view the thread, then you can see all four
> attachments: cavity.sh, cavity.gfs, cavity.gfv, isotherms.gfv. I
> suppose this is a quirk or bug in the SourceForge e-mail archive.
> I'll in-line the original files below, to stop it happening again.
>
> Quickly running them again, I see that they may be a little old. In
> particular:
>
> 1. the syntax for comments seems to have changed? Delete the comments
> on the GfsSource and GfsInit lines.
>
> 2. Also the GfsSourceDiffusion statements generate warnings. Replace
> them with a viscosity statement.
>
> 3. There's a warning from gfsview-batch2D, so I guess the cavity.gfv
> needs to be regenerated (by running gfsview interactively, setting up
> the desired image which is just a linear hue plot of temperature T
> between zero and one, and saving as a .gfv file).
>
> Just doing (1) makes it run O.K.
>
> The eventual steady state problem is based on the benchmark
> discussed by
>
> de Vahl Davis, G. (1983). Natural convection of air in a square
> cavity: A benchmark numerical solution. International Journal for
> Numerical Methods in Fluids 3 (3), 249-264.
>
> http://dx.doi.org/10.1002/fld.1650030305
>
> %<---cavity.sh
> gerris2D cavity.gfs | gfsview-batch2D cavity.gfv
> echo "Save isotherms.eps { format = EPS }" | gfsview-batch2D cavity-
> end.gfs isotherms.gfv
> convert -delay 10 $(ls -rt cavity-*.ppm) cavity.mpg && rm -f cavity-
> *.ppm
> %<---cavity.gfs
> 1 0 GfsSimulation GfsBox GfsGEdge {} { # the square cavity is a GfsBox
>
> GfsSourceDiffusion {} U (sqrt (0.71 / 1e6))
> GfsSourceDiffusion {} V (sqrt (0.71 / 1e6))
>
> GfsVariableTracer {} T # the temperature
> GfsSourceDiffusion {} T (1.0 / sqrt (1e6 * 0.71))
> GfsSource {} V T # beta = 1
> GfsInit {} { T = 0.5 } # for centrosymmetric evolution
>
> ## Up till t=1e2, adapt on temperature gradient, then fix the
> grid so
> ## that we can use GfsEventStop to detect a steady temperature
> field.
>
> GfsRefine 7
> GfsAdaptGradient { istep = 1 end = 1e2 } {
> maxlevel = 7 minlevel = 4 cmax = 5e-2
> } T
>
> GfsEventStop { istep = 10 start = 1e2 } T 5e-4 DT
>
> GfsOutputTime { istep = 1 end = 1e2 } evolution
> GfsOutputBalance { istep = 1 end = 1e2 } evolution
> GfsOutputScalarNorm { istep = 10 start = 1e2 } evolution { v = DT }
>
> GfsOutputSimulation { step = 1 } stdout { variables = T }
> GfsEventScript { step = 1 } {
> echo "Save cavity-$GfsTime.ppm { width = 256 height = 256
> format = PPM }"
> }
> GfsOutputSimulation { start = end } cavity-end.gfs {
> variables = U,V,P,T
> }
>
> }
> GfsBox {
>
> top = Boundary {
> BcDirichlet U 0
> BcDirichlet V 0
> }
> bottom = Boundary {
> BcDirichlet U 0
> BcDirichlet V 0
> }
> right = Boundary {
> BcDirichlet U 0
> BcDirichlet V 0
> BcDirichlet T 0.0
> }
> left = Boundary {
> BcDirichlet U 0
> BcDirichlet V 0
> BcDirichlet T 1.0
> }
> }
> %<---cavity.gfv
> # GfsView 2D
> View {
> tx = 0 ty = 0
> q0 = 0 q1 = 0 q2 = 0 q3 = 1
> fov = 30
> r = 0.3 g = 0.4 b = 0.6
> res = 1
> lc = 0.001
> reactivity = 0.1
> }
> Linear {
> r = 0 g = 0 b = 0
> shading = Constant
> maxlevel = -1
> } {
> n.x = 0 n.y = 0 n.z = 1
> pos = 0
> } T {
> min = 0
> max = 1
> cmap = Jet
> } {
> scale = 0
> }
> %<---isotherms.gfv
> # GfsView 2D
> View {
> tx = 0 ty = 0
> q0 = 0 q1 = 0 q2 = 0 q3 = 1
> fov = 30
> r = 0.3 g = 0.4 b = 0.6
> res = 1
> lc = 0.001
> reactivity = 0.1
> }
> Isoline {
> r = 0 g = 0 b = 0
> shading = Constant
> maxlevel = -1
> } {
> n.x = 0 n.y = 0 n.z = 1
> pos = 0
> } T {
> amin = 0 min = 0
> amax = 0 max = 1
> cmap = Jet
> } {
> n = 11
> }
> Cells {
> r = 0 g = 0 b = 0
> shading = Constant
> maxlevel = 0
> } {
> n.x = 0 n.y = 0 n.z = 1
> pos = 0
> }
>
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----> ----> ----> ----> ----> ---->
attention, pyl et lmm disparaissent:
----> ----> ----> ----> ----> ---->
---> Pierre-Yves Lagrée (PYL)
-->www.lmm.jussieu.fr/~lagree
-> pierre-yves.lagree@...
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