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


  • 管理员

    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 = 2
    Ck/Ce
    delta^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


登录后回复
 

与 CFD中文网 的连接断开,我们正在尝试重连,请耐心等待