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Adding a constitutive differential equation via an UDF

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Old   January 2, 2024, 07:35
Smile Adding a constitutive differential equation via an UDF
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Hello everyone


I want to model a special kind of diffusion with Ansys Fluent where one of the governing differential equations has a structure which is not very common, hence I can't use any of the provided model's equations as a surrogate.


The equation looks as follows:

\frac{\partial m_{11}}{\partial t} = \frac{J_s}{\rho(1-c)} \frac{\partial m_{11}}{\partial x} - m_{11}\frac{\partial}{\partial x}(\frac{J_s}{\rho(1-c)}) - K_1(K_2 m_{11}-1)

m_11 is the governing variable with it's time evolution playing a crucial part in the model. J_s is the diffusion flux, which will be model via the dilute approximation (hopefully) regarding species transport. Additionally, m_11 is included in one of the other equations, for completeness sake here they are:

J_s = -\rho D(\frac{\partial c}{\partial x} + \Gamma\frac{\partial m_{11}}{\partial x})

and

\rho\frac{\partial c}{\partial t} = -\frac{\partial J_s}{\partial x}

My question is the following: Can I implement a non-linear partial differential equation via an UDF with one of the inputs, J_s, being the diffusion flux calculated by Fluent via the dilute approximation?


Thanks in advance,
bambino
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differential equations, diffusion, udf and programming


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