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Spalart - Allmaras Turbulence Jacobian

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Old   July 21, 2010, 16:55
Question Spalart - Allmaras Turbulence Jacobian
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Hello everyone,

I am trying to implement the SA turbulence model to an existing NS solver with FEM, where the NS and SA governing equations will be solved at the same time, coupled. I am having trouble in deriving the Jacobian for the SA equation.

I think the derivative of the NS equations with respect to turbulent viscosity Nu^tilde is zero. If the last row of the residual is the SA residual, the last column of the NS-part of the Jacobian is all zero (4 zeros for 2D case). But I am having trouble in calculating the derivative of the SA equation with respect to the states. I am using conservative variables (Rho , Rho*v_j , Rho*E, Rho*Nu^tilde) to define the equations.

Any help would be appreciated.
Thanks.
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