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IDProjectCategoryView StatusDate SubmittedLast Update
0000255OpenFOAMBugpublic2011-07-18 16:502011-07-23 18:49
Reporteruser231Assigned Tohenry  
PrioritynormalSeveritytweakReproducibilityN/A
Status resolvedResolutionfixed 
PlatformLinuxOSUbuntuOS Version10.04
Summary0000255: missing coefficient
DescriptionIn homogeneousDynSmagorinsky.C, the definition of cD seems inconsistent with the derivation of Lilly (1992). In Lilly's paper, there is an extra '2' coefficient in the denominator of equation 11 which is not seen in the openfoam implementation. The homogeneousDynSmagorinsky.C implementation is consistent with Fureby et al. (1997), however, the '2' coefficient in front of the Mij term seems to mysteriously vanish in Fureby's derivation between equations 6 and 7.
Steps To ReproduceN/A
Additional InformationLilly, D.K., 1992, A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids, 4, 633-635.

C. Fureby, G. Tabor, H. G. Weller, and A. D. Gosman, 1997, A comparative study of subgrid scale models in homogeneous isotropic turbulence, Phys. Fluids, 9, 1416.
TagsNo tags attached.

Activities

henry

2011-07-19 12:19

manager   ~0000565

The cD in the homogeneousDynSmagorinsky model corresponds to 2*C in Lilly's paper which is convenient because then the factor of 2 in the expression for nuSgs is not required, i.e.

nuSgs = cD*delta^2*||D||

and

cD=<L.M>/<M.M>

are consistent. If you believe otherwise and think there is actually an error in the homogeneousDynSmagorinsky model please reopen this thread and provide details.

user231

2011-07-19 14:32

  ~0000568

I apologize for the ambiguity of my initial explanation. I will try to be more explicit. I will label my own equations here, some copied directly from the code, with '(#)'

OpenFOAM accounts for the turbulent and molecular deviatoric stresses in the incompressible solvers using the divDevReff (RAS) or divDevBeff (LES) term:

(1)
tmp<fvVectorMatrix> GenEddyVisc::divDevBeff(volVectorField& U) const
{
    return
    (
      - fvm::laplacian(nuEff(), U) - fvc::div(nuEff()*dev(T(fvc::grad(U))))
    );
}

where the effective viscosity 'nuEff' is the sum of the molecular viscosity and 'eddy viscosity'

(2)
virtual tmp<volScalarField> nuEff() const
{
    return tmp<volScalarField>
    (
        new volScalarField("nuEff", nuSgs() + nu())
    );
}

the turbulent stresses are thus interpreted as:
(3) tau = -2 * nuSgs * D
(4) D = 0.5 * (grad(U) + grad(U).T())
(5) divDevBeff = div(tau)

this is all good and fine with me so far
(the trace of the gradient tensor is zero by continuity for incompressible flows)

from the homogeneousDynSmagorinsky code:

(6) const volSymmTensorField D(dev(symm(gradU))); // as defined above in eqn (4)
(7) cD(D) = average(LL && MM)/MMMM;
(8)
const volSymmTensorField MM
(
    sqr(delta())*(filter_(mag(D)*(D)) - 4*mag(filter_(D))*filter_(D))
);
(9) nuSgs_ = cD(D)*sqr(delta())*sqrt(magSqr(D));

therefore, piecing it together from eqns (3) and (9)

(10) tau = -2 * cD(D) * sqr(delta()) * sqrt(magSqr(D)) * D

which is the same as Lilly et al (1992) equation 5, and the MM term is consistent with Lilly's equation 9
(to be exact, it differs by a factor of sqrt(2) from the sqrt(magSqr(D)) term, but this is accounted for because the MM equation also differs from Lilly's equation 9 by the same factor, hence cD(D) differs from Lilly's definition by the reciprocal)

therefore, I am of the opinion that the definition of cD(D) in eqn (8) should include the leading coefficient of 1/2 as in Lilly's equation 11.

I hope that I was more clear this time.

Regards,
Perry

henry

2011-07-19 14:44

manager   ~0000569

If the cD includes the 1/2 coefficient then the nuSgs expression would need the factor of 2:

nuSgs = cD*2*delta^2*||D||

what would be the advantage of first dividing by 2 and then multiplying by 2?

user231

2011-07-19 14:55

  ~0000570

the '2' coefficient you suggest is not needed because it is already there (implicitly) in the divDevBeff equation, see equation (1) and (3) above

henry

2011-07-23 18:49

manager   ~0000587

Thanks for the clarification. I have now had time to study the relevant papers and I agree with your finding and applied the appropriate correction:
commit 90da72aa43cdb7f795f9abb3a522f0455f07b73d

Thanks for reporting.

Issue History

Date Modified Username Field Change
2011-07-18 16:50 user231 New Issue
2011-07-19 12:19 henry Note Added: 0000565
2011-07-19 12:19 henry Status new => closed
2011-07-19 12:19 henry Assigned To => henry
2011-07-19 12:19 henry Resolution open => fixed
2011-07-19 14:32 user231 Note Added: 0000568
2011-07-19 14:32 user231 Status closed => feedback
2011-07-19 14:32 user231 Resolution fixed => reopened
2011-07-19 14:44 henry Note Added: 0000569
2011-07-19 14:55 user231 Note Added: 0000570
2011-07-19 14:55 user231 Status feedback => assigned
2011-07-23 18:49 henry Note Added: 0000587
2011-07-23 18:49 henry Status assigned => resolved
2011-07-23 18:49 henry Resolution reopened => fixed