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I have just learned basic FEM for 2D N-S euqation, now my teacher let me to do the following problem, the document of this problem is in large fluid problem, the system of equations is listed in that page, I don't even know what is the boundary condition, could you please recommend some textbooks or papers for solving the following system of equations by using FEM?thank you very much.$$ \begin{aligned} \partial_t \theta+u \nabla \theta-\nabla \cdot\left(\kappa_T^m \nabla \theta\right) & =0 \\ \partial_t u+u \nabla u-\nabla \cdot\left(\mu_T \nabla u\right)+\nabla p+e\left(\theta-\theta_0\right) \vec{e}_2 & =0 \\ \nabla \cdot u & =0 \\ \mu_T & =c_\mu \frac{k^2}{\epsilon} \\ \kappa_T & =\kappa \mu_T \\ \partial_t k+u \nabla k+\epsilon-\nabla \cdot\left(\mu_T \nabla k\right) & =\frac{\mu_T}{2}\left|\nabla u+\nabla u^T\right|^2 \\ \partial_t \epsilon+u \nabla \epsilon+c_2 \frac{\epsilon^2}{k}-\frac{c_\epsilon}{c_\mu} \nabla \cdot\left(\mu_T \nabla \epsilon\right) & =\frac{c_1}{2} k\left|\nabla u+\nabla u^T\right|^2 \end{aligned} $$ I want to know the boundary conditions, choose of element, method of transform the nonlinear term to linear term,could you please recommend some books or papers, thank you

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  • $\begingroup$ This is called the $k$-$\varepsilon$ set of equations for modeling turbulence. Have you looked at books that describe turbulence modeling? $\endgroup$ Jan 23 at 18:16
  • $\begingroup$ I have found one detailed book $\endgroup$
    – 吴yuer
    Jan 23 at 20:37

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