Isometric Collision Rules for the Four-Dimensional FCHC Lattice Gas

Collision rules are present ed for th e four-dimensional facecentered-hypercubic-lattice (FCHC) . The velocity set after collision is deduced from th e velocity set be fore collision by an isometry, chosen so as to preserve th e momentum and minimiz e the viscosity. A detailed implementation recipe is given. Th e shea r viscosity is camputed; th e result shows that essentially all memory of t he previous velocities is lost at each collision. Anot her set of collision rules, based on a random choice of the output state, has similar pr ope rties . The isometric prin cipl e can also be applied to t he two-dimension al squar e (HPP) and triangular (FHP) latti ces : one recovers t he usual rule s with minor differences.