LATTICE FLUID-DYNAMICS FROM PERFECT DISCRETIZATIONS OF CONTINUUM FLOWS

We use renormalization group methods to derive equations of motion for large scale variables in fluid dynamics. The large scale variables ar e averages of the underlying continuum variables over cubic volumes an d naturally exist on a lattice. The resulting lattice dynamics represe nts a perfect discretization of continuum physics, i.e., grid artifact s are completely eliminated. Perfect equations of motion are derived f or static, slow Rows of incompressible, viscous fluids. For Hagen-Pois euille flow in a channel with a square cross section the equations red uce to a perfect discretization of the Poisson equation for the veloci ty field with Dirichlet boundary conditions. The perfect large scale P oisson equation is used in a numerical simulation and is shown to repr esent the continuum flow exactly. For nonsquare cross sections one can use a numerical iterative procedure to derive Bow equations that are approximately perfect. [S1063-651X(98)04511-5].