of1612+里面的smagorinsky的k equation是怎样推导的
-
Reference: \verbatim Smagorinsky, J. (1963). General circulation experiments with the primitive equations: I. The basic experiment*. Monthly weather review, 91(3), 99-164. \endverbatim The form of the Smagorinsky model implemented is obtained from the k-equation model assuming local equilibrium which provides estimates of both k and epsilon separate from the sub-grid scale viscosity: \verbatim B = 2/3*k*I - 2*nuSgs*dev(D) where D = symm(grad(U)); k from D:B + Ce*k^3/2/delta = 0 nuSgs = Ck*sqrt(k)*delta \endverbatim
实在是看不太懂里面这个D:B + Ce*k^3/2/delta = 0是如何得来的
-
看起来好像方程18:http://dyfluid.com/LES.html
@李东岳
k from D:B + Ce*k^3/2/delta = 0
在哪体现的?
-
smagorinsky.c
template<class BasicTurbulenceModel> tmp<volScalarField> Smagorinsky<BasicTurbulenceModel>::k ( const tmp<volTensorField>& gradU ) const { volSymmTensorField D(symm(gradU)); volScalarField a(this->Ce_/this->delta()); volScalarField b((2.0/3.0)*tr(D)); volScalarField c(2*Ck_*this->delta()*(dev(D) && D)); return tmp<volScalarField> ( new volScalarField ( IOobject ( IOobject::groupName("k", this->U_.group()), this->runTime_.timeName(), this->mesh_ ), sqr((-b + sqrt(sqr(b) + 4*a*c))/(2*a)) ) ); }
-
@赵一铭
D:B + Ce*k^3/2/delta = 0 is used
to calculate k_SGS in smagorinsky, which is rather different from earlier version.
-
Ce*k^3/2/delta is used to calculate epsilon
-
nuSgs = Cksqrt(k)delta
k = 2Ck/Cedelta^2*(D&&D),which is used in earlier version
the second term on the rhs
Cek^3/2/delta = 2Ckdeltak^1/2*(D&&D)=2nuSgs(D&&D)thus
D:B + Cek^3/2/delta = (2/3kI)&&D + 2nuSgs*((D-dev(D))&&D) =(2/3kI)&&D+2/3nuSgs(tr(D)&&D)in the end k = -nuSgs*tr(D)??? get puzzled