Theory

Governing equations

Enter governing equations here.

Discretized equations

Discretization

Let consider a scalar partial differential equation (PDE) solving for a variable \(w\):

(3)\[\partial_t w + \vec{u} \cdot \nabla w = q,\]

The scalar PDE given in Eq. 3 is function of a velocity \(\vec{u}\) and a volumetric source term \(q\).

Boundary conditions

Enter boundary conditions here.

Initial conditions

Eneter initial conditions here.