HowTo Adding a new transport equation

Suppose you want to solve and additional scalar transport equation for the scalar $\psi$ by adding it to an existing solver. The equation has the form

$\frac{\partial}{\partial t} \left(\rho \psi \right) + \nabla \cdot \phi \psi - \nabla \cdot \Gamma \nabla \psi = S_{\psi}$

where $\rho$ and $\Gamma$ are defined as dimensionedScalar and are retrieved from a dictionary using the lookup member function. $S_{\phi}$ is the source term.

To implement the equation, just add the line:

dimensionedScalarField psi;

to the createFields.H file of the solver,

Then, solve the equation by adding the following lines in the point of the solver where you want the equation to be solved.

 
solve
(
    fvm::ddt(rho, psi)
  + fvm::div(phi, psi)
  - fvm::laplacian(gamma, psi)
  ==
    S_psi
);

In this example, the source term is treated explicitly. To manage it implicitly, OpenFOAM provides the Sp and the SuSp functions. Suppose we can write it as $S_k = \Kappa \psi$. The code lines to solve the same equation with an implicit treatment of the source term are:

 
solve
(
    fvm::ddt(rho, psi)
  + fvm::div(phi, psi)
  - fvm::laplacian(gamma, psi)
  ==
    fvm::Sp(kappa, psi)
);

SuSp(kappa, psi) can be used to discretise the source term implicitly or explicitly according to the sign of kappa.