ICAMS / Interdisciplinary Centre for Advanced Materials Simulation


Discrete kinetic theory: Lattices and entropy

Date: 09.11.2016
Time: 11:00 a.m.
Place: ICAMS Seminar-Room, IC 02-722

Santosh Ansumali, Department of Engineering Mechanics, Jawaharlal Nehru Centre for Advanced Scientific Research

Abstract: The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, structured grid approach of LBM is often preferred due to its flexibility and better parallel scaling. In this talk, I will argue that the choice of lattice in LBM is not optimal and significant speed-up can happen by a proper choice of lattice. I will argue that Body Centered Cubic arrangement of grid points provides a more natural set-up for formulating LBM.

I will also present a new formulation of LBM where H-theorem (second law of thermodynamics) exist in explicit form for a discrete space-time model. I will argue that the second law of thermodynamics provides a new way to formulate non-linearly stable numerical numerical methods for hydrodynamics. This new formulation provides next generation entropic LBM, where non-linear stability is achieved without compromising on the simplicity of standard LBM. Using these improvements, I will illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of Direct numerical simulation for realistic flows.

Finally, I will comment on possibility of utilizing ideas developed in context of mesoscale methods to speed up other computational methods of statistical physics. As an example, I will illustrate a new algorithm, ``Molecular Dice'' to generate Guassian and Uniform random numbers.

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