FDS Convergence
Randy McDermott
Thanks for your inquiry. In the long run, this is indeed an important
issue to consider in FDS. So that I hit all the points in your
discussion, let me go through them one by one. Then I will have some
general comments at the end.
1. As soon as possible you should start working with FDS 5.
2. There is no explicit "filtering and averaging procedure" in FDS.
FDS is an "implicit" LES code.
3. There is no such thing as "optimal resolution" in LES. I
understand what is meant in this context, but we should get away from
such notions.
4. An explicit LES formulation is simply a set of PDEs for the
filtered fields (e.g. \bar{u}_i), and all notions of "conventional
convergence" apply.
5. For an implicit LES formulation there is no guarantee of monotonic
convergence unless: (a) the LES formulation reduces to a DNS in the
limit of vanishing filter width, and (b) the smaller of the viscous
and diffusive length scales are well-resolved (i.e. you are performing
a DNS). Now, for the sake of efficiency, the FDS developers have
decided, at the present time, not to formulate the equations in such a
way that they reduce to DNS in the limit of vanishing filter width
(grid spacing in the case of implicit LES with Delta = h, where Delta
is the filter width and h is the grid spacing). In the long run, the
correct way to fix this issue is to develop subgrid models that tend
to zero as h tends to zero. Then there will be no need for an "LES
mode" and a "DNS mode" in FDS. Absolutely the wrong way to address
this issue is to use introduce ad hoc features to the "LES mode" of
FDS.
6. Concerning your statement about the "correct grid size," the only
way to make any LES model "complete" (i.e. free from artificial
parameters like the filter width) is by implementing adaptive mesh
refinement (AMR). This issue is discussed at length in Pope (New
Journal of Physics, 2004).
7. Regarding your comment about making a guess for the right values of
Delta and Cs, the LES community has been studying the constant
coefficient Smagorinsky model for over 50 years; there is no need to
guess at Delta and Cs. In FDS, Delta = h. For the constant
coefficient model, Cs = 0.2 in the bulk flow and 0.05 in channel flow.
This is confirmed by theory (Lilly, 1967) and numerous experiments
and DNS studies. Improvements to the FDS turbulence model will come
by implementing the dynamic procedure (Germano, Moin, etc., 1990s) for
computing Cs. This procedure has been established for more than a
decade. There is no new research to be done here. A key advantage of
the dynamic model is that it vanishes as the filter width tends to
zero, and it does so at the correct second-order rate (as established
by Leonard). Further, it is important that these models be used in
conjunction with kinetic energy-conserving numerical schemes. There
are some minor improvements that can be made to FDS in this area, but
for the most part the numerics are very sound.
General comments:
Somewhere on the FDS web page Kevin has posted a "road map" which
discusses what he thinks are the top priorities for improving FDS as a
fire model (not as an academic LES code). I don't think he puts this
convergence issue up there as a top priority. You and he and discuss
this if you want. I do not have the experience or authority to decide
the order of priorities for FDS. However, to address the converge
issues I can tell you that FDS needs to make the following
modifications:
(A) LES to DNS convergence. If subgrid-scale models are properly
designed, then these terms will vanish as Delta = h tends to zero, and
they will do so at a second-order rate (Leonard). Here is where using
the dynamic model for Cs would be helpful. There are some tricks to
implementing this model that make it just at cheap to use as the
constant coefficient model. My guess is that previously when people
have tried to implement the dynamic model into FDS they have used an
inefficient implementation and this has led to the conclusion that it
is too expensive. This is not true, however; it is sufficient to
compute the coefficient on say every 10th time step or more and this
makes up for the added expense.
(B) Improvements to scalar transport. The scalar transport scheme is
bounded, but it is not total variation diminishing (TVD). This could
be a big reason why you do not see good convergence properties at
coarse resolutions. It would take only minor modifications to make
the scheme TVD. I have everything worked out, but it is low on the
priority list.
(C) Adaptive Mesh Refinement. In the long run, AMR is the only way to
make an LES code "complete," i.e., free from artificial (non-physical)
parameters like the filter width. Further, AMR is obviously an
natural fit for a fire/structure model because the active domain of
the fire is moving in space and time as the simulation proceeds. It
is easy to realize that any future state-of-the-art fire model will
necessarily incorporate AMR. Experience has shown that for fire
capturing more modes with a low-order (second-order) code yields
superior a posteriori results than using higher-order numerics ("H"
refinement over "P" refinement); hence, second-order AMR is a natural
fit for FDS.
I hope this addresses some of your questions. To reiterate, I think
it is best to take a long term approach to fixing these problems, not
to key in on one particular convergence study and then play with the
"LES mode" of FDS until you get it to work. There are very sound
guiding principles to designing an LES code, and these need to be
considered in conjunction with the efficiency of the code.
Best regards,
Randy
p.s. If you respond to the group, please also include my email
address, as I do not check the discussion board on a daily basis.
Cheers...
On Jan 4, 2008 6:41 AM, Dipl.-Ing. D. Toris <d.t...@uni-wuppertal.de> wrote:
> Dear Mr. McDermott,
>
> i am working since some time at the convergence behavior of FDS v4.0.
> I think its very interesting to can explain how the filtering and
> averaging procedure works in FDS.
> Because Kevin says that one should beginn with a coarse grid and try
> to find an optimal resolution in the sense that
> the results shows not appreciable changes after a certain reduced grid size.
> But i think tha one can not expect such an conventional convergence
> behavior from an LES-code because there are no conservation equations
> for the turbulence quantities like k and epsilon in RANS-modells and
> with finer grids more details of the flow are resolved and so a greater
> portion of the kinetic energy are directly computed. I have conduct
> some studies and he shows that the convergence is not monotonic.
> I think for fire simulation it is not meaningfull to look for the
> right grid size with convergence studies. The right grid size may be
> a function of both, the local turbulence intensity and the Smagorinsky
> Constant.
> I have asked Bryan Klein at the Interflam Conference in London and he
> has suggested that i should talk about this with you.
> I think it makes sense, to understand the tubrulence modell in FDS and
> to make some guess for the right values for Delta and
> Cs we must first define a simple modell from which we can think that
> it does the same work like the FDS-Code. So we can formulate
> at this simple modell some working hypotheses and try than to validate
> these with simulations on the main code.
> I hope that you are interested at this topic and that we can work
> together with other people for this goal.
>
> best regards
> Dimitrios
>
> --
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> Bergische Universität
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>
dr_jfloyd
> i am working since some time at the convergence behavior of FDS v4.0.
> I think its very interesting to can explain how the filtering and
> averaging procedure works in FDS.
> Because Kevin says that one should beginn with a coarse grid and try
> to find an optimal resolution in the sense that
> the results shows not appreciable changes after a certain reduced grid size.
calc to determine a some set of quantities for some fire protection
purpose. For example one might be interested in how long adequate
visibility is maintained along an exit path. For such problems a grid
study is quite useful. Yes, as the grid is more refined there will be
more structure resolved within the fire plume and the ceiling jet and
clearly there will never be a point were instanteous quantities
converge at a particular location. However, there will certainly be a
point where more grid cells will not result in any appreciable change
to the time available for egress.
Validation work shows that we do a pretty good job with moving around
hot gasses. How much better would we do with any added expense to the
hydrodynamic solver? Would the improvement be enough to justify the
cost (algorithm development, coding, testing, V&V, additional
computational/memory cost, missed opporutnities {development
resources, i.e. number of things that can be done at once, are
limited }).?
On Jan 4, 11:42 am, "Randy McDermott" <randy.mcderm...@gmail.com>
wrote:
>
> - Show quoted text -
Randy McDermott
From: Randy McDermott <randall....@nist.gov>
Date: Jan 4, 2008 4:11 PM
Subject: Re: FDS Convergence
To: "Dipl.-Ing. D. Toris" <d.t...@uni-wuppertal.de>, Kevin McGrattan
<kevin.m...@nist.gov>
Dimitrios:
I understand your English fine. It's much better than my German!
But, it is important that we get some definitions straight.
First, "implicit" LES and "numerical" LES are NOT the same. In
implicit LES we use energy-conserving numerical schemes and
physically-based subgrid models. In numerical LES, there is no
concept of a physical subgrid model; the DNS equations are solved
using TVD numerical schemes and the dissipation introduced by the
numerics is responsible for keeping the code stable. FDS is NOT
numerical LES; it is implicit, physical LES. It would be worthwhile
for you to take a look at Pope's "10 Questions" paper:
http://eccentric.mae.cornell.edu/~tcg/pubs/Pope_NJP_04.pdf. Not
everything is covered there, but it is a good reference. If you are
going to be working heavily in LES, you should also be thoroughly
familiar with his book (S. B. Pope. Turbulent Flows. Cambridge, 2000).
For a discussion of energy-conserving numerical schemes, see
Morinishi et al. (JCP, 1998) and Ham et al. (JCP, 2002).
Now, in principle, with an implicit LES code you can turn off the
subgrid closure and the molecular viscosity and the numerics will
conserve energy for a canonical problem like unforced turbulence in a
periodic domain. This is not true of numerical LES codes. This makes
implicit (kinetic energy-conserving) LES much more desirable because
we can actually think about the physics when we construct the subgrid
models. Even though it is true that the truncation error for the PDE
is of the same order as the subgrid model (see Ghosal, JCP 1996), i.e.
it is not negligible, we must understand that in practical codes the
leading-order physics of the subgrid model is the transfer of energy
between resolved and unresolved scales. In this sense, the
leading-order physics is correctly captured for the implied kinetic
energy equation (this equation can be derived from your numerical
scheme, see Morinishi or Ham). The experience of the LES community
over the past decade has been that when using energy-conserving
numerics with physically-based subgrid models (like Smagorinsky)
turbulent statistics can be captured accurately, even though the
numerical solution of the LES PDE quickly diverges from true solution
(the system is chaotic).
Regarding your second point, personally I think it is a mistake to
look at FDS as a whole and then try to decide on the "best" grid
resolution. This will be completely problem dependent and in my mind
provides no real benefit to the community. It would more beneficial
to look at each subgrid model in FDS individually and construct a
model problem that exercises only that particular part of FDS. Then
show how the specific residual terms in the FDS model behave as the
grid is refined. If they do not asymptote to zero at the proper rate
for that given model, then there is room for improvement. I can tell
you that you are wasting your time playing with the Smagorinsky
constant in an effort to tune the FDS results. As I mentioned
previously, the Smagorinsky model is well understood. Assuming there
is not a bug in the code, whatever problems you are experiencing lie
elsewhere.
I hope this can help you refine your search for the root of the
convergence problem.
Best regards,
Randy
On Jan 4, 2008 2:52 PM, Dipl.-Ing. D. Toris <d.t...@uni-wuppertal.de> wrote:
> Randy,
>
> thank you very much for your very detailed answer which adresses much
> of my questions.
> Because i am still not a member of the discussion group and i am not
> sure about my knowledge of the english language i prefer the email
> contact with you for the moment.
> Now some comments to your reply:
>
> 1. You say that FDS is an "implicit" LES-code. I think that is the
> same as if one would say that FDS is an "numerical" LES-code. At this
> point i have a question, because i thought first exactly the same as
> the typical grid resolutions of 10cm which is established for fire
> simulations with fds is not fine enough to hold the numerical error
> negliglible. But the PDEs in FDS are written for a filtered quantity
> for example through the reposition at the right hand side of the
> momentum equation of the pressure term through the filtered
> fluctuating pressure term and the decoupling of the divergence term
> from the momentum equation. Second you have placed on the right hand
> side of the momentum equation the effective viscosity (as a product of
> the Smagorinsky constant, the grid spacing and the strain rate), so an
> explicit modell which contains the filter width appears at your
> momentum equation. In numerical LES the only "model" should be the
> numerical error and the dumping characteristic of the insufficient
> grid resolution. That is the reason why i think that FDS is somethink
> between physical (explicit) and numerical (implicit) LES. (of course i
> can not say that i am an expert at this field!).
>
> 2. I have the same opinion with you, that we should not use the
> conventional notation like as "convergence" or "optimal resolution"
> but other FDS-users may believe that FDS behaves like an conventional
> RANS-code. That is why i think that it is essential to eplain to the
> FDS-community why there is a different way to get good results for i
> relative low cost (=coarse grid resolution). It is not my intention to
> implement an improved LES-modell but to understand how FDS works. At
> the moment i conduct some studies with ever finer grids to see how the
> filtering of the velocity fields varies with variable grid spacing h
> and smagorinsky constant. I think that the default value of the
> smagorinsky constant (cs=0,2) corresponds to a grid spacing of arround
> 10cm. But as the computer power increases and the parallel processing
> option became available in FDS the possibility that one would use a
> very small grid spacing together with the default value for the
> smagorinsky constant would lead to unaccurate results and that a finer
> grid not absolutely leads to better results.
>
> I will discuss the other points of your reply with my collegues here
> (A. Seyfried and C. Rogsch) and if there is some question i would
> writte to you a message.
> I am sorry for my bad english! I am very happy finding a person with
> which i can talk about the turbulence modelling in FDS. Thank you very
> much Randy!
Boris Stock
read.
Please hold it public as long as possible so others can participate in
your discussion.
Boris
Dimitrios
of a few centimeters (say 10cm) one can run FDS as a "numerical" LES,
that is without physical subgrid modell?
Kevin
no LES sub-model, regardless of cell size.