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Nonlinear Transient Term

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Old   July 17, 2019, 16:35
Default Nonlinear Transient Term
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I would like to solve one equations system as follows:

\frac{\partial \phi_1}{\partial t} + \nabla \cdot (\textbf{v} \phi_1 ) = 0 (Eq. 1)

\frac{\partial (\phi_1 \phi_2 + f(\phi_2))}{\partial t} + \nabla \cdot (\textbf{v} \phi_2 ) = 0 (Eq. 2)

where f(\phi_1) is a nonlinear function (e.g. f(\phi_2) = \phi_2 e^{\phi_2}).

How may I implement this system in the OpenFOAM. My main problem is handling the nonlinear term. Can I write this piece of code:

Solve ( fvm::ddt(phi_1) + fvc::div(v,phi_1) );

Solve ( fvm::ddt(phi_1*phi_2+f(phi_2)) + fvc::div(v,phi_2) ); or Solve ( fvm::ddt(phi_1*phi_2) + fvm::ddt(f(phi_2)) + fvc::div(v,phi_2) );

I assumed the velocity field is known. Thanks in advance.
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implementing new solver, nonlinear terms, system coupling

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