sandbox/b-flood/darcy.h

    Darcy friction for Saint-Venant

    When the Reynolds number is high (>2000), the stream becomes turbulent and the friction can no longer be obtained analytically. Darcy and Weisbach proposed an empirical relation describing the corresponding friction. It can be written in its full form as: \displaystyle C_f = \frac{f}{8} \frac{q|q|}{h^2}, where f, the “Darcy coefficient”, is a free-parameter wich depends on the nature of the soil.

    double f = 0.5; 

event darcy_friction (i++)
{
  foreach()
    if (h[] > dry)
      foreach_dimension()
	u.x[] /= 1 + dt*f*norm(u)/(8*h[]);
  boundary ((scalar *){u});
}