Lattice Hydrodynamics

@article{Sullivan2018LatticeH,
  title={Lattice Hydrodynamics},
  author={Dennis Sullivan},
  journal={arXiv: Analysis of PDEs},
  year={2018}
}
  • 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. 

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References

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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