[Nek5000-users] Variable density flows

[nek5000-users at lists.mcs.anl.gov]

Hi Praveen,

The only way to guarantee monotonicity when under-resolved
is to effectively increase viscosity; whether it be uniformly
or locally (preferred).   This is still an active area of 
research.   If I were in your place, I would clip until I 
found a better strategy... (something still foremost in my
mind).

Note that upwinding, limiters, and the recent (and promising)
entropy viscosity method all achieve monotonicity or near-monotonicity
via (local) dissipation.  (With limiters it's not clear that you're diffusing,
but in effect that is what happens.)


Paul


----- Original Message -----
From: nek5000-users at lists.mcs.anl.gov
To: "nek5000" <nek5000-users at lists.mcs.anl.gov>
Sent: Monday, November 4, 2013 11:22:04 PM
Subject: Re: [Nek5000-users] Variable density flows




These tips are most useful. I am able to run some high Re and high Pe cases but I still need really large meshes to ensure that the scalar stays bounded between [0,1]. 


Is the characteristic time stepping going to be useful for these cases ? I have read that it allows larger time steps. Since "characteristic" means some upwind effect, I was wondering does it help to maintain better monotonicity of advected scalars ? 


Thanks 
praveen 


On Mon, Oct 14, 2013 at 12:37 AM, < nek5000-users at lists.mcs.anl.gov > wrote: 



Hi Praveen, 

Your clipping implementation will as you have it -- I normally would 
do it in a single loop: 

n=nx1*ny1*nz1*nelt 
do i=1,n 
t(i,1,1,1,2)=min(1.,t(i,1,1,1,2)) 
t(i,1,1,1,2)=max(0.,t(i,1,1,1,2)) 
enddo 

You can turn on filtering by setting param(103) in your .rea file. 
Setting p103=.05, say, would reduce the energy in the Nth mode by 
5% each timestep --- this is usually a good choice. Sometimes it 
pays to bump this up to, say, .1, but usually a better strategy is 
to add another mode to the filter, by setting p101 to 1, or 2. 
In this case, the filter amplitude for the N-1 mode is alpha/4 
when p101=1 and when p101=2, we have amplitudes as: 

a(N) = alpha := p103 
a(N-1) = alpha*(2/3)**2 = 4*alpha/9 
a(N-2) = alpha*(1/3)**2 = alpha/9 

which amounts to fitting a parabola through the filter amplitudes so 
that the filter strength decays smoothly to zero. 

p103 = .05 
p101 = 1 

are my common choices when lx1=8. If lx1 < 8, I typically set p101=0 
as you're otherwise cutting too deeply into low end of the spectrum. 

All this being said, you'll no doubt still need clipping if Sc=100,000. 


Paul 


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