sandbox/gally/SFD_stream.h

Selective Frequency Damping method in the stream-vorticity form

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)

Because it has to be integrated at each time step : - \delta t\cdot\chi(\mathbf{q}^n_i-\mathbf{\bar{q}}^n_i)

Code

scalar omegabar[];

SFD’s control parameters :

double SFD_Delta;
double SFD_chi;

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

Calculation of the SFD’s control parameters.

event init (i = 0, last) {
 
  SFD_Delta = 1/(M_PI*freq_SFD);
  SFD_chi = 1/SFD_Delta;

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

  foreach()
    omegabar[] = omega[];
}

Calculation of the correction term and of the next step’s filtered field.

event SFD (i++) {
  foreach() {
    omega[] += SFD_toggle ? - dt * SFD_chi * (omega[] - omegabar[])/2. : 0.;
    omegabar[] = (omega[] - omegabar[]) * (dt/SFD_Delta) + omegabar[];
  }
}