View source for HowTo Adding a new transport equation

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

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

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

To implement the equation, just add the line:

<cpp>dimensionedScalarField psi;</cpp>

to the <tt>createFields.H</tt> 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.

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

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

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

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

[[Category:Tutorials]]