From Molecular Dynamics to lattice Boltzmann

Lattice Boltzmann methods have been hugely successful for the simulation of fluid systems at the Navier-Stokes level, but for phenomena bejond Navier-Stokes (like fluctuating systems) it is often unclear how to correctly incorporate those effects. We will show that is is possible to directly derive lattice gas and lattice Boltzmann from Molecular Dynamics throught a coarse-graining procedur [1]. Doing so leads to the definition of novel integer lattice gases [2,3,4] and  shows that standard assumptions regarding fluctuations are often incorrect [5]. It can also establish a physical justification for the so called "over-relaxation" process [7], which in turn justifies the definition of integer lattice gas methods with such a collision operator [4].

[1] M. Reza Parsa and Alexander J. Wagner, Lattice gas with molecular dynamics collision operator, Phys. Rev. E 96, 013314 (2017)

[2] Thomas Blommel and Alexander J. Wagner, Integer lattice gas with Monte Carlo collision operator recovers the lattice Boltzmann method with Poisson-distributed fluctuations

      Phys. Rev. E 97, 023310  (2018)

[3] Noah Seekins and Alexander J. Wagner, Integer lattice gas with a sampling collision operator for the fluctuating diffusion equation,  Phys. Rev. E 105, 035303 (2022)

[4] Kyle Strand and Alexander J. Wagner, Overrelaxation in a diffusive integer lattice gas, Phys. Rev. E 105, L063301 (2022)

[5] M. Reza Parsa, Changho Kim, and Alexander J. Wagner, Nonuniqueness of fluctuating momentum in coarse-grained systems, Phys. Rev. E 104, 015304 (2021)

[6] M. Reza Parsa and Alexander J. Wagner, Large Fluctuations in Nonideal Coarse-Grained Systems, Phys. Rev. Lett. 124, 234501 (2020)

[7] Aleksandra Pachalieva, Alexander J. Wagner, Connecting lattice Boltzmann methods to physical reality by coarse-graining Molecular Dynamics simulations, arXiv:2109.05009