The flow equations consist of the mass conservation equation

$\nabla\cdot {\bf u}=q$

and the Darcy law

${\bf u} =- \frac{1}{\mu}K\nabla p.$

Here, ${\bf u}$ denotes the velocity and $p$ the pressure. The permeability tensor is given by $K$ and $\mu$ denotes the viscosity.

We solve the flow equations for a Cartesian grid and we set the source term $q$ be zero except at the left-lower and right-upper corner, where it is equal with opposite sign (inflow equal to outflow).

Program walk-through.

We construct a Cartesian grid

    int dim = 3;
    int nx = 40;
    int ny = 40;
    int nz = 1;
    Opm::GridManager grid(nx, ny, nz);