manning.h

Friction term : Manning in saint venant

Friction term : Manning in saint venant

When the Reynolds number is high (>2000), the stream becomes turbulent. In this case, the friction term can’t be easily solved analytically. Manning proposed an empirical law describing this term, it can be written in its full form as : \displaystyle Cf = - n^2 g \frac{q|q|}{h^{7/3}} where n is a free-parameter wich depends on the nature of the soil.

The overloading process is fully explained in poiseuille.h

// Manning coefficient
double n = 0.025;

We define the function which will replace the update function in the predictor-corrector

void updatemanning(scalar * evolving, scalar * sources, double dtmax, int numbersource ){
  // We first recover the evolving fields
  scalar h = evolving[0];
  vector u = { evolving[1], evolving[2] };
  
  // Updates for evolving quantities
  vector dshu = { sources[1], sources[2] }; 

  foreach(){
    if(h[] > dry){

We Compute the new field u with an implicit scheme. The u^2 term is linearised

      double s = dtmax*n*n*G*norm(u)/pow(h[],4./3.);
      foreach_dimension()
	// Translate it in an explicit form
	dshu.x[] -= h[]*u.x[]*s/(s+1)/dtmax;
    }
  }
  // Calling of the next source term
  numbersource++;
  updatesource[numbersource](evolving,sources,dtmax,numbersource);
}

// Overloading 
event initmann(i = 0){
  updatesource[numbersource]=updatemanning;
  numbersource++;
  updatesource[numbersource] = fnull;
}