In fluid dynamics, one often performs discretization of Navier-Stokes equation to do numerical simulation of hydrodynamics. As the governing equations are non-linear and non-local, one often needs very large-scale simulations and advanced algorithms to deal with non-local pressure term in modern distributed computing environments. The lattice Boltzmann model (LBM), a discrete space time kinetic theory has emerged as an alternate efficient parallel method to describe fluids dynamics in sub-sonic regime in isothermal conditions. However, in the transition from Boltzmann equation to discrete space-time kinetic theory of LBM, much was gained but two key features were lost – namely, the H Theorem and unconditional numerical stability. In this talk, I will review Entropic LB models which were proposed when people came to realize that these two lost features were closely related. Entropic LB models restore nonlinear stability to the methodology by restoring H Theorem in a discrete space-time setting. This constructive procedure to build thermodynamics at a discrete level is equivalent to an implicit turbulence model. This constructive procedure is taken further, and LBM is formulated on the body centered cubic grid. I argue that this lattice provides an optimal compromise between the accuracy of unstructured mesh and the efficiency of a based scheme. This move provides enormous flexibility to formulate higher order LBM for transonic and strongly thermal flows.
As a second example of discrete models, we consider the problem of generating random numbers with pre-specified distribution. I show that simplified particle-based simulations of dilute gas system also provide an opportunity to generate sequences of random numbers from the trajectory. The central hypothesis is that Maxwells Demon, which we perceive as an omniscient being holding the knowledge of each particle's position and velocity, is a generator of random sequences. As to an observer not privy to these details, these state variables will seem apparently random as it arises from the chaotic motion of the particles.
Ref:
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Atif, M. et al., "Essentially entropic lattice Boltzmann model", Phys. Rev. Lett. 119, 240602(2017).
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Namburi, M. et al.,"Crystallographic Lattice Boltzmann Method", Sc. Reports, 27172 (2016).
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Agrawal, et al., "Molecular Dice: Random number generators a la Boltzmann ", ´ Phys. Rev. E 98, 063315 (2018).
Biosketch:
Dr. Santosh Ansumali, is a Professor at Engineering Mechanics Unit at the Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR) Bangalore. He is also the founder of Sankhyasutra Labs, Bangalore and was its CTO in year 2019-2021. Before his stint as a Professor at JNCASR, Dr. Ansumali was an Assistant Professor between 2005-2009 in the department of chemical and biomedical engineering at the Nanyang Technological University, Singapore. He did his B.Sc. in chemical engineering from the Bihar Institute of Technology in 1998 and his M.E. in chemical engineering from the Indian Institute of Science, Bangalore, in 2000. He received his Ph.D. from the Institute of Polymer Physics, Department of Materials, ETH Zurich in 2004, and completed his postdoc from the Department of Energy Technology, ETH Zurich, in 2005.
Dr. Ansumali's research interests include mesoscale simulation Methods, kinetic theory, and high-performance computing. In particular, his focus in the last decade was the development of the entropic lattice Boltzmann method for the simulation of fluid flows. This formulation is regularly used in commercial as well as popular open source codes such as palabos and openlb. His group has helped create a large scale code for direct numerical simulation of hydrodynamics using lattice Boltzmann method. These efforts led to the creation of SankhyaSutra Lab and its multiphysics simulation platform. His work in COVID19 research and planning was an important starting point for India's supermodel for COVID19.
Dr. Ansumali is a recipient of CNR oration award 2022, A.P.J Abdul Kalam HPC Award by HP-CRAY in 2020, Ramanujan fellowship in 2009 and ETH gold medal in year 2004.
Dr. Santosh Anusmali is the first recipient of the 'IIT Bombay International Award for Excellence in Research in Engineering & Technology'. The award includes a cash prize of Rs.10 lakhs & a citation.