====== $k$-$ε$モデル ======
==== $k$-$ε$ model ====

{{tag>..c01}}

　渦粘性係数を，乱流エネルギー//k//とその散逸率//ε//で表す代表的な二方程式乱流モデル．レイノルズ応力\(\overline {{u_i}{u_j}} \)は，次式で表す．\[ - \overline {{u_i}{u_j}}  = \nu_i \left( {\partial {{\bar U}_i}/\partial {x_j} + \partial {{\bar U}_j}/\partial {x_i}} \right) - 2{\delta _{ij}}k/3\]渦粘性係数//ν<sub>t</sub>//は，乱れの速度を//k//<sup>1/2</sup>で，乱れの空間スケールを//L<sub>e</sub>//＝//k//<sup>3/2</sup>///ε//で代表させ，\({\nu _t} = C\mu {k^{1/2}}Le = C\mu {k^2}/\varepsilon \)と置く．//k//と//ε//は次式から求める．\[\begin{array}{l} {D_k}/D\tau  = {D_k} + {P_k} - \varepsilon \\ D\varepsilon /D\tau  = {D_\varepsilon } + \left( {\varepsilon /k} \right)\left( {{C_{\varepsilon 1}}{P_k} - {C_{\varepsilon 2}}\varepsilon } \right) \end{array}\]ここで，\({D_k} = \partial \left[ {\left( {{\nu _t}/{\sigma _k}} \right)\partial k/\partial {x_j}} \right]/\partial {x_j}\)(拡散)，\({P_k} =  - \overline {{u_i}{u_j}} \partial {\bar U_i}/\partial {x_j}\)(生成)，\({D_\varepsilon } = \partial \left[ {\left( {{\nu _t}/{\sigma _\varepsilon }} \right)\partial \varepsilon /\partial {x_j}} \right]/\partial {x_j}\)(拡散)
〔応力方程式モデル〕


~~NOCACHE~~