Lattice Fluid Dynamics from Perfect Discretizations of Continuum Flows ∗
نویسنده
چکیده
We use renormalization group methods to derive equations of motion for large scale variables in uid dynamics. The large scale variables are averages of the underlying continuum variables over cubic volumes, and naturally live on a lattice. The resulting lattice dynamics represents a perfect discretization of continuum physics, i.e. grid artifacts are completely eliminated. Perfect equations of motion are derived for static, slow ows of incompressible, viscous uids. For Hagen-Poiseuille ow in a channel with square cross section the equations reduce to a perfect discretization of the Poisson equation for the velocity eld with Dirichlet boundary conditions. The perfect large scale Poisson equation is used in a numerical simulation, and is shown to represent the continuum ow exactly. For non-square cross sections we use a numerical iterative procedure to derive ow equations that are approximately perfect.
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