Complex Systems

Isometric Collision Rules for the Four-Dimensional FCHC Lattice Gas Download PDF

Michel Hénon
C.N.R.S., Observatoire de Nice,
B.P. 139, 06003 Nice Cedex, France


Collision rules are presented for the four-dimensional face-centered-hypercubic- lattice (FCHC). The velocity set after collision is deduced from the velocity set before collision by an isometry, chosen so as to preserve the momentum and minimize the viscosity. A detailed implementation recipe is given. The shear viscosity is computed; the result shows that essentially all memory of the previous velocities is lost at each collision. Another set of collision rules, based on a random choice of the output state, has similar properties. The isometric principle can also be applied to the two-dimensional square (HPP) and triangular (FHP) lattices: one recovers the usual rules with minor differences.