Short note: Isotropic discrete Laplacian operators from lattice hydrodynamics

  • Authors:

  • Sumesh P. Thampi;Santosh Ansumali;R. Adhikari;Sauro Succi

  • Affiliations:

  • Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India;Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India;The Institute of Mathematical Sciences, CIT Campus, Chennai 600113, India;Istituto Applicazioni Calcolo, CNR Roma - via dei Taurini 9, 00185 Roma, Italy

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2013

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Abstract

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.