  The author investigates the onset of patterns in vertically oscillated layers
of dissipative particles using numerical solutions of continuum equations to
Navier-Stokes order. Above a critical accelerational amplitude of the cell,
standing waves form stripe patterns which oscillate subharmonically with
respect to the cell. Continuum simulations neglecting interparticle friction
yield pattern wavelengths consistent with experiments using frictional
particles. However, the critical acceleration for standing wave formation is
approximately 10% lower in continuum simulations without added noise than in
molecular dynamics simulations. This report incorporates fluctuating
hydrodynamics theory into continuum simulations by adding noise terms with no
fit parameters; this modification yields a critical acceleration in agreement
with molecular dynamics simulations.

Soft Condensed Matter