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Finite volume method applied on Spalart-Allmaras model
We decided to use the Spalart-Allmaras model without transition corrections ( 
). Finite volume method can be applied on Spalart-Allmaras transport equation by the analogical way:
![$\displaystyle \frac{\partial \tilde{\nu}}{\partial t} = -\frac{1}{{\mathsf {D}}} \oint_{\partial V} \Big[ \tilde{\nu} v \Big] d\vec{n} + \frac{1}{\sigma {\mathsf {D}}} \oint_{\partial V} \Big[ (\nu + \tilde{\nu}) \frac{\partial \tilde{\nu}}{\partial x_j} \Big] d\vec{n} + C_{b1} \tilde{S} \tilde{\nu} + \frac{1}{\sigma} C_{b2} \frac{\partial \tilde{\nu}}{\partial x_j} \frac{\partial \tilde{\nu}}{\partial x_j} - C_{w1} f_w \Big( \frac{\tilde{\nu}}{d_w} \Big)^2$](https://www.cfdsupport.com/wp-content/uploads/2022/02/img516.png "Node399 8") | (27.34) |