Lattice Hydrodynamics

  title={Lattice Hydrodynamics},
  author={Dennis Sullivan},
  journal={arXiv: Analysis of PDEs},
  • D. Sullivan
  • Published 31 October 2018
  • Mathematics
  • arXiv: Analysis of PDEs
Using the combinatorics of two interpenetrating face centered cubic lattices together with the part of calculus naturally encoded in combinatorial topology, we construct from first principles a lattice model of 3D incompressible hydrodynamics on triply periodic three space. Actually the construction applies to every dimension, but has special duality features in dimension three. 

Figures from this paper


3D incompressible fluids: Combinatorial models, Eigenspace models, and a conjecture about well-posedness of the 3D zero viscosity limit
where X is a divergence free vector field (i.e., incompressible), Y = curlX, and [ , ] is the Lie bracket which is our nonlinear structure. This equation states that the vorticity of the fluid motionExpand
Sur le mouvement d'un liquide visqueux emplissant l'espace