Lattice differential operators for computational physics

Ramadugu, Rashmi; Thampi, Sumesh P.; Adhikari, R.; Succi, Sauro; Ansumali, Santosh

doi:10.1209/0295-5075/101/50006

Cited by 28 publications

(26 citation statements)

References 26 publications

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“…This lattice calculus of integer order is defined on a general triangulating graph by using discrete field quantities and differential operators roughly analogous to differential forms and exterior differential calculus. A scheme to derive lattice differential operators of integer orders from the discrete velocities and associated Maxwell-Boltzmann distributions that are used in lattice hydrodynamics has been suggested in the articles [51,52]. In this paper to formulate a lattice fractional calculus, we use other approach that is based on models of physical lattices with long-range inter-particle interactions and its continuum limit that are suggested in [41,42,25] (see also [43][44][45][46][47][55][56][57][58][59]).…”

Section: Introductionmentioning

confidence: 99%

Lattice fractional calculus

Tarasov

2015

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Lattice fractional calculus

Tarasov

2015

Applied Mathematics and Computation

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“…[14], we have measured that in our case the effective diffusivity stays well below a 2% difference with the nominal diffusivity D, for the comparably low value used here D = 0.01, and the largest possible fluid velocities. Previous researchers have performed careful comparisons of the accuracy of different differential operators, revealing that higher lattice connectivities indeed increase the accuracy and convergence (as a function of the resolution), although total errors are expected to be negligible in our cases of variations on the order of the diffusive interface [31].…”

Section: A Hydrodynamicsmentioning

confidence: 74%

Mesoscopic electrohydrodynamic simulations of binary colloidal suspensions

Rivas

Frijters

Pagonabarraga

et al. 2018

The Journal of Chemical Physics

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A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a Bhatnagar-Gross-Krook collision operator using the lattice Boltzmann method to simulate binary fluid flows. Solvent-solvent and solvent-solute interactions are implemented using a pseudopotential model. The Nernst-Planck equation, describing the kinetics of dissolved ion species, is solved using a finite difference discretization based on the link-flux method. The colloids are resolved on the lattice and coupled to the hydrodynamics and electrokinetics through appropriate boundary conditions. We present the first full integration of these three elements. The model is validated by comparing with known analytic solutions of ionic distributions at fluid interfaces, dielectric droplet deformations, and the electrophoretic mobility of colloidal suspensions. Its possibilities are explored by considering various physical systems, such as breakup of charged and neutral droplets and colloidal dynamics at either planar or spherical fluid interfaces.

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“…Finally, we have inspected the computational time to steady-state for a given accuracy, at changing the size of the problem and the order of the quadrature. By combining the previous relations, (30) and (31), we obtain:…”

Section: Computational Performancementioning

confidence: 86%

High-order kinetic relaxation schemes as high-accuracy Poisson solvers

Mendoza

Succi

Herrmann

2015

Int. J. Mod. Phys. C

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We present a new approach to find accurate solutions to the Poisson equation, as obtained from the steady-state limit of a diffusion equation with strong source terms. For this purpose, we start from Boltzmann's kinetic theory and investigate the influence of higher order terms on the resulting macroscopic equations. By performing an appropriate expansion of the equilibrium distribution, we provide a method to remove the unnecessary terms up to a desired order and show that it is possible to find, with high level of accuracy, the steady-state solution of the diffusion equation for sizeable Knudsen numbers. In order to test our kinetic approach, we discretise the Boltzmann equation and solve the Poisson equation, spending up to six order of magnitude less computational time for a given precision than standard lattice Boltzmann methods.

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Lattice differential operators for computational physics

Cited by 28 publications

References 26 publications

Lattice fractional calculus

Lattice fractional calculus

Mesoscopic electrohydrodynamic simulations of binary colloidal suspensions

High-order kinetic relaxation schemes as high-accuracy Poisson solvers

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