/*?This?is?a?standard?two?dimensional?lattice?Boltzmann?program?with
???periodic?boundary?conditions?that?should?perform?reasonably?efficiently.
???It?has?been?written?for?teaching?purposes?by?Alexander?Wagner
???at?NDSU?（March?2003）.?
*/

#include?
#include?
#include?
#include??/*?for?the?sleep?function.?this?may?not?be?standard?*/
#include?
#include?

#define?xdim?31
#define?ydim?21

#define?DEBUG

double?f0[xdim][ydim]
??f1[xdim][ydim]f2[xdim][ydim]f3[xdim][ydim]f4[xdim][ydim]
??f5[xdim][ydim]f6[xdim][ydim]f7[xdim][ydim]f8[xdim][ydim];

#ifdef?DEBUG
double?b1[xdim][ydim]b3[xdim][ydim]b5[xdim][ydim]b6[xdim][ydim]
??bb[xdim][ydim];
#endif

double?omega=1;

/*?Some?constants?that?appear?often?and?don‘t?need?to?be?calcula