filter.h

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/** @file filter.h
 */
/**
# Fourth-order filter
 
This is not ready for general consumption. Just kept for reference. */
 
double filter = 1./16.; // maximum filtering for fourth-order filter, see Klemp
 
/** @brief Event: viscous_term (i++) */
void event_viscous_term (void) 
{
  // fourth-order filter
#if dimension == 1
  for (int _i = 0; _i < _N; _i++) /* foreach */
    foreach_layer()
      for (int _s = 0; _s < 1; _s++) /* scalar in {w,u} */
  s[] -= (s[2] + s[-2] - 4.*(s[1] + s[-1]) + 6.*s[])*filter;
#else // dimension == 2
  // this is the 4th-order diagonal-term operator of [Klemp, 2017](#klemp2017)
  for (int _i = 0; _i < _N; _i++) /* foreach */
    if (x > 114 && x < 169 && y > 10 && y < 65)
    foreach_layer()
      for (int _s = 0; _s < 1; _s++) /* scalar in {w,u} */
        s[] -= ((s[2,2] + s[2,-2] + s[-2,-2] + s[-2,2])/16. +
    (s[-1,2] + s[1,2] + s[-1,-2] + s[1,-2] +
     s[2,-1] + s[2,1] + s[-2,-1] + s[-2,1])/4. +
    3.*(s[2,0] + s[-2,0] + s[0,2] + s[0,-2])/8. -
    (s[1,1] + s[1,-1] + s[-1,-1] + s[-1,1]) -
    5.*(s[1,0] + s[-1,0] + s[0,1] + s[0,-1])/2. +
    41.*s[]/4.)*filter;
#endif // dimension == 2
}
 
/**
## References
 
~~~bib
@article{klemp2017,
  title={Damping characteristics of horizontal Laplacian diffusion filters},
  author={Klemp, Joseph B},
  journal={Monthly Weather Review},
  volume={145},
  number={11},
  pages={4365--4379},
  year={2017}
}
~~~
*/