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Derivative of two volScalarFields

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Old   November 16, 2017, 05:35
Default Derivative of two volScalarFields
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Jan Gaertner
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I am trying to implement the Homogeneous Relaxation Model (HRM) of Downar-Zapolski (1995) in interPhaseChangeFoam.
Currently I am struggling with the pressure equation and explicitly the derivative of two volScalarFields \frac{\partial \rho}{\partial \alpha} which is the derivative of the density to the phase fraction alpha.
Is there already a built in function in OpenFoam or do I have to write my own method for this?
I could not find anything on the forum or in the manual. All gradients I found are only gradients in space.

The derived pressure equation is:
\rho \nabla \cdot \left(\frac{\nabla p}{a_p}\right) - \rho \nabla \cdot \left(\frac{H(U)}{a_p}\right) =  \left(\frac{\partial \rho}{\partial \alpha}\right)_{p,h} \underbrace{\left(   -\alpha  \frac{h_\mathrm{ML}(p,T)-h_\mathrm{SL}(p)}{h_\mathrm{SG}(p)-h_\mathrm{SL}(p)}\frac{1}{\Theta}\right)}_{\frac{\mathrm{D}\alpha}{\mathrm{D}t}}

This pressure equation can also be found in the work of Lee et al. (Flashing flow of superheated jet fuel) and Schmidt (Multi-dimensional simulation of thermal non-equilibrium channel flow)
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derivatives, gradient, interphasechangefoam, volscalarfield

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