Cellular automata and massively parallel physics
C. E. Leith · NASA STI/Recon Technical Report N · 1989
A cellular a u tom a ton (CA) has been proposed I as an effective compute r for fluid flows and t h u s for t u r b u l e n c e s imula t ions . One d e d u c e s macroscop ic h y d r o d y n a m i c m o t ion by s imula t ing c rude ly b u t efficiently on a CA the microscopic dynamics of molecules in a gas and t h e n averaging the results . Unfortunately, bad molecular dynamics gives poor hydrodynamics 2,3. The best known difficulties are the lack of Galilean invariance, the large and ill-defined viscosity, the velocity dependen t equat ion of state, stat ist ical problems of low Mach number , and the need for a wastefully low density. In addi t ion to these more obvious problems there are subtle difficulties coming to light. For example, McNamara and Zanet t i 4 have discovered false m o m e n t u m integrals in the hexagonal lattice gas which are more obscure t h a n those in the square lattice gas. Colvin, Ladd. and Alder 5 find for the lattice gas an unrealist ic approach to the 1 / t long-time tail of two-dimensional molecular dynamics , b u t th i s is improved in the i r maximal ly discret ized molecu la r dynamics (MDMD) of colliding hard hexagons on a CA at no great difference in cost. Much progress has been repor ted at this meet ing in reducing these problems and finding the modera te Reynolds n u m b e r domain where a CA may be useful. Even ff the CA hydrodynamics were good, it is noisy by the statist ical na ture of the under lying process. It is necessary to average over the molecular motions to get hydrodynamic variables; the averaging has inevitable sampling errors; for these to be modera te the sample mus t be large; and it t u rns out tha t the bit manipu la t ions in a CA space-t ime averaging block m ay be pu t to bet ter use in floating point opera t ions at the corresponding single spacet ime grid point in convent ional Navier-Stokes solvers 2. A s i m p l e w a y to get rid of the noise is to car ry a probabil i ty ra the r t han a bit for each molecular state on the lattice. The bit collision rules are now