Origin of spurious oscillations in lattice Boltzmann simulations of oscillatory noncontinuum gas flows

Yong Shi, Daniel R. Ladiges, John E. Sader

Research output: Journal PublicationArticlepeer-review

6 Citations (Scopus)


Oscillatory noncontinuum gas flows at the micro and nanoscales are characterized by two dimensionless groups: A dimensionless molecular length scale, the Knudsen number Kn, and a dimensionless frequency θ, relating the oscillatory frequency to the molecular collision frequency. In a recent study [Shi, Phys. Rev. E 89, 033305 (2014)10.1103/PhysRevE.89.033305], the accuracy of the lattice Boltzmann (LB) method for simulating these flows at moderate-to-large Kn and θ was examined. In these cases, the LB method exhibits spurious numerical oscillations that cannot be removed through the use of discrete particle velocities drawn from higher-order Gauss-Hermite quadrature. Here, we identify the origin of these spurious effects and formulate a method to minimize their presence. This proposed method splits the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation into two equations: (1) a homogeneous "gain-free equation" that can be solved directly, containing terms responsible for the spurious oscillations; and (2) an inhomogeneous "remainder equation" with homogeneous boundary conditions (i.e., stationary boundaries) that is solved using the conventional LB algorithm. This proposed "splitting method" is validated using published high-accuracy numerical solutions to the linearized Boltzmann BGK equation where excellent agreement is observed.

Original languageEnglish
Article number053317
JournalPhysical Review E
Issue number5
Publication statusPublished - 25 Nov 2019

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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