1
2
6
5
4
3

Previous: Finite volume method applied Up: Spalart – Allmaras model Next: Model’s initial and boundary

This is an automatically generated documentation by LaTeX2HTML utility. In case of any issue, please, contact us at info@cfdsupport.com.

System of governing equations including Spalart-Allmaras model

  •   The system of governing equations was simply completed by one differential (transport) equation supporting eddy viscosity. The system can be rewritten in the following form:
    $\displaystyle \left( \begin{array}{c} 0 \\ u \\ v \\ \tilde{\nu} \\ \end{array} \right)_{t}+ \left( \begin{array}{c} u \\ u^2 + p \\ uv \\ u\tilde{\nu} \\ \end{array}\right)_{x} + \left( \begin{array}{c} v \\ vu \\ v^2 + p \\ v\tilde{\nu} \\ \end{array}\right)_{y} =\left( \begin{array}{c} 0 \\ (\nu + \nu_T) u_x \\ (\nu + \nu_T) v_x \\ \frac{\nu + \tilde{\nu}}{\sigma}\tilde{\nu}_x \\ \end{array}\right)_{x} +\left( \begin{array}{c} 0 \\ (\nu + \nu_T) u_y \\ (\nu + \nu_T) v_y \\ \frac{\nu + \tilde{\nu}}{\sigma}\tilde{\nu}_y \\ \end{array}\right)_{y} + Q$ (27.35)
    where the source member Q has following meaning:
    $\displaystyle Q = \left( \begin{array}{c} 0 \\ 0 \\ 0 \\ C_{b1} \tilde{S} \tilde{\nu} + \frac{1}{\sigma} C_{b2} \frac{\partial \tilde{\nu}}{\partial x_j} \frac{\partial \tilde{\nu}}{\partial x_j} - C_{w1} f_w \Big( \frac{\tilde{\nu}}{d_w} \Big)^2 \\ \end{array}\right)$ (27.36)
OpenFOAM Training by CFD Support,   CFD SUPPORT,   info@cfdsupport.com    +420 212 243 883      © CFD support, s.r.o., Sokolovská 270/201, 190 00 Praha 9, Czech Republic