src/test/higuera.c

    Viscous hydraulic Jump

    We want to reproduce the hydraulic jump of Higuera (1994).

    #include "grid/cartesian1D.h"
#include "saint-venant.h"

int main() {
  X0 = 0.14;
  L0 = 1. - X0;
  G  = 1.;
  N  = 128;
  nl = 15;
  nu = 1.;
  run();
}

    We impose boundary condition for h and \eta.

    h[left] = dirichlet (.2);
eta[left] = dirichlet (.2);

h[right] = dirichlet (0.02);
eta[right] = dirichlet (0.02);

    Initialization

    We define a scalar field hc to check for convergence on h.

    scalar hc[];

event init (i = 0) {

    We set a constant velocity at the inlet and a free outlet.

      for (vector u in ul) {
    u.n[left] = 5.5;
    u.n[right] = neumann(0.);
  }

    We initialize h and hc.

      foreach()
    hc[] = h[] = 0.2;
}

    We check for convergence.

    event logfile (t += 0.1; i <= 10000) {
  double dh = change (h, hc);
  printf ("%g %g\n", t, dh);
  if (i > 0 && dh < 1e-5)
    return 1;
}

    Output

    We print the elevation and the stress.

    event output (t = end) {
  vector u0 = ul[0];
  foreach()
    fprintf (stderr, "%g %g %g\n", x, eta[], 2.*u0.x[]/(h[]/nl));
}

    Results

    X0 = 169
X1 = 604
Y0 = 222.24
Y1 = 528
unset tics
plot [0:][0:605] 'higuera.png' binary filetype=png with rgbimage not, \
  'log' u (X0+$1*(X1-X0)):($2/2*(Y1-Y0)+Y0) t 'h' w l,		      \
  '' u (X0+$1*(X1-X0)):($5/15*(Y1-Y0)+Y0) t 'tau' w l
    Comparison with Figure 2 of Higuera (1994). (script)

    Bibliography