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    如何隐式离散应变率张量

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    • T
      thw1021 last edited by

      请教大家一个问题。
      如果将雷诺应力按如下方式分解
      $$
      \boldsymbol{\tau}^{m}=\nu_{t}^{L} \mathbf{S}+\left(\boldsymbol{\tau}-\boldsymbol{\tau}^{L}\right)+\operatorname{tr}(\boldsymbol{\tau})
      $$
      其中$\nu_{t}^{L}$可以理解为湍流涡黏系数(但有所不同)。$\mathbf{S}=\frac{1}{2}\left[\nabla \mathbf{U}+(\mathbf{\nabla} \mathbf{U})^{T}\right]$是应变率张量(strain-rate tensor)。
      如果要求$\mathbf{S}$隐式离散,在OpenFOAM中应该如何实现?(The strain rate tensor $\mathbf{S}$ is treated implicitly in the modified flow solver.)

      我个人的理解:
      以不可压缩流动为例,OpenFOAM-7中对应的雷诺应力计算方式为:

      template<class BasicTurbulenceModel>
      Foam::tmp<Foam::fvVectorMatrix>
      Foam::linearViscousStress<BasicTurbulenceModel>::divDevRhoReff
      (
          volVectorField& U
      ) const
      {
          return
          (
            - fvc::div((this->alpha_*this->rho_*this->nuEff())*dev2(T(fvc::grad(U))))
            - fvm::laplacian(this->alpha_*this->rho_*this->nuEff(), U)
          );
      }
      

      因此,只有$\nabla \mathbf{U}$是隐式离散,而$(\mathbf{\nabla} \mathbf{U})^{T}$其实是显式离散的。并且也没有直接使用$\mathbf{S}$,相当于是把 $2\mathbf{S}$ 做了分解。

      如果要对$\mathbf{S}$进行隐式离散,是不是应使用fvm::div() ?
      $\nu_{t}^{L} \mathbf{S}$ 应该如何表示 ?

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      • 李东岳
        李东岳 管理员 last edited by

        @thw1021 在 如何隐式离散应变率张量 中说:

        The strain rate tensor S is treated implicitly in the modified flow solver.

        所以文章里面把$\nabla\bfU^T$隐性离散了?

        CFD课程 改成线上了 http://dyfluid.com/class.html
        CFD高性能服务器 http://dyfluid.com/servers.html

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        • T
          thw1021 last edited by thw1021

          @李东岳 至少论文里面是这样说的。The strain rate tensor S is treated implicitly in the modified flow solver.

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