User:MasterHD/Turbulent Energy Dissipation Rate

A two-equation k-$$\epsilon$$ turbulence model commonly used in modern engineering applications uses the following two additional differential equations to close the RANS equation,


 * $$ \frac{\partial K}{\partial t}+\bar\upsilon_j \frac{\partial K}{\partial x_j} = {\mathcal P} -\epsilon+\nu\nabla^2 K -\frac{\partial}{\partial x_i} \left ( \frac{\overline{p \upsilon_i^\prime}}{\rho}+\overline{\upsilon_i^\prime(\upsilon_j^{\prime\, 2}/2)} \right) $$


 * $$ \frac{\partial \epsilon}{\partial t}+\bar\upsilon_j\frac{\partial \epsilon}{\partial x_j}=P_\epsilon^1+P_\epsilon^2+P_\epsilon^3+P_\epsilon^4+\Pi_\epsilon+T_\epsilon+D_\epsilon-\Upsilon_\epsilon$$