1202.3299 (Sumesh P. Thampi et al.)

Isotropic discrete Laplacian operators from lattice hydrodynamics    [PDF]

Sumesh P. Thampi, Santosh Ansumali, Ronojoy Adhikari, Sauro Succi

We show that discrete schemes developed for lattice hydrodynamics provide an
elegant and physically transparent way of deriving Laplacians with isotropic
discretisation error. Isotropy is guaranteed whenever the Laplacian weights
follow from the discrete Maxwell-Boltzmann equilibrium since these are, by
construction, isotropic on the lattice. We also point out that stencils using
as few as 15 points in three dimensions, generate isotropic Laplacians. These
computationally efficient Laplacians can be used in cell-dynamical and hybrid
lattice Boltzmann simulations, in favor of popular anisotropic Laplacians,
which make use of larger stencils. The method can be extended to provide
discretisations of higher order and for other differential operators, such the
gradient, divergence and curl.

View original: http://arxiv.org/abs/1202.3299