sandbox/gally/SFD.h

Selective Frequency Damping method

The low-pass filtered version of the initial flow is calculated at each iteration using an Euler explicite scheme (\Delta a control parameter of the method) : \mathbf{\bar{q}}^{n+1}_i \simeq \left( \mathbf{q}^n_i-\mathbf{\bar{q}}^n_i \right) \frac{\delta t}{\Delta} +\mathbf{\bar{q}}^n_i

The flow is then forced by adding to the acceleration term (\chi the second control parameter) : -\chi(\mathbf{q}^n_i-\mathbf{\bar{q}}^n_i)

Code

Variables that should be defined in the user’s main .c code :

double freq_SFD; // frequency of the instability to kill (approximative)
bool SFD_toggle; // conditions for activation of the SFD

SFD’s control parameters

double SFD_Delta;
double SFD_chi;

vector ubar[];
scalar pbar[];

av[] the correction term is imposed as the acceleration.

face vector av[];
event defaults (i = 0) {
  a = av;
}

We set the initial conditions for the filtered flow, they should be the same as the calculated flow.

event init (i = 0, last) {
  
  SFD_Delta = 1/(M_PI*freq_SFD);
  SFD_chi = 1/SFD_Delta;
  
  foreach() {
    foreach_dimension()
      ubar.x[] = u.x[];
    pbar[] = p[];
  }
}

We add the SFD correction term to the acceleration.

event acceleration (i++) {
  foreach_face()
    av.x[] = SFD_toggle ? - SFD_chi * ((u.x[] - ubar.x[]) + (u.x[-1] - ubar.x[-1]))/2. : 0.;
}

We calculate the next step’s filtered field.

event bar (i++) {
  foreach() {
    foreach_dimension()
      ubar.x[] = (u.x[] - ubar.x[]) * (dt/SFD_Delta) + ubar.x[];
    pbar[] = (p[] - pbar[]) * (dt/SFD_Delta) + pbar[];
  }
}