Effects of Thermal Noise on Pattern Onset in Continuum Simulations of Shaken Granular Layers

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.