How to discretize the governing equations of the dynamic wake model?

Dear all,
I’m learning the dynamic wake model of fast.farm, it is known that the control equation is solved by Thomas algorithm in the code to obtain Vx_ wake。 But I don’t know how to discretize the governing equations to get the values of a (j), b (j), c (j) and d (j) in the matrix?? Does anyone know the derivation process of the specific formula? Can you provide some references?

Best Wishes!

YuanMing Yuan

Dear YuanMing Yuan,

The theory basis of FAST.Farm is documented in the online OpenFAST readthedocs documentation: 4.2.13.7. FAST.Farm Theory — OpenFAST v3.1.0 documentation. This theory basis explains the analytical expressions for the conservation of mass and conservation of momentum and mentions the finite difference schemes used for each. However, the exact finite-difference equations are not spelled out here. We do have these in an unpublished FAST.Farm implementation plan that I can share with you if you are interested.

Best regards,

Dear Jason.Jonkman,

Thank you for your reply. I have checked the official public documents many times, and they cannot solve the problem I am currently raising. I hope you can share the exact finite-difference equations. My email is 837115242@qq.com

Best regards,
YuMing Yuan

Dear YuMing Yuan,

I’ve sent you via e-mail the FAST.Farm implementation plan, valid for OpenFAST v3.0, that includes the exact finite-difference equations used for the conservation of mass and conservation of momentum (among other details).

Best regards,

Dear Jason.Jonkman,

I did a quick read and this is exactly the information I was looking for, thanks for your help.

Best regards,
YuMing Yuan

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