Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1997-09-12
Physics
High Energy Physics
High Energy Physics - Lattice
25 pages, tex., using epsfig, minor changes, refernces added
Scientific paper
10.1103/PhysRevE.58.5796
We use renormalization group methods to derive equations of motion for large scale variables in fluid 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 flows of incompressible, viscous fluids. For Hagen-Poiseuille flow in a channel with square cross section the equations reduce to a perfect discretization of the Poisson equation for the velocity field with Dirichlet boundary conditions. The perfect large scale Poisson equation is used in a numerical simulation, and is shown to represent the continuum flow exactly. For non-square cross sections we use a numerical iterative procedure to derive flow equations that are approximately perfect.
Katz Eric
Wiese Uwe-Jens
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