Discontinuous Galerkin discretizations of the Boltzmann-BGK equations for nearly incompressible flows: Semi-analytic time stepping and absorbing boundary layers

Karakus A., Chalmers N., Hesthaven J. S., Warburton T.

JOURNAL OF COMPUTATIONAL PHYSICS, vol.390, pp.175-202, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 390
  • Publication Date: 2019
  • Doi Number: 10.1016/j.jcp.2019.03.050
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.175-202
  • Keywords: Perfectly matching layer, Semi-analytic, Multirate, Boltzmann equation, Discontinuous Galerkin, GPU, PERFECTLY MATCHED LAYER, RUNGE-KUTTA SCHEMES, HIGH-ORDER, CONSTRUCTION, COMPUTATIONS, ELEMENT, EULER, SIMULATION, MODEL
  • Middle East Technical University Affiliated: No


We present an efficient nodal discontinuous Galerkin method for approximating nearly incompressible flows using the Boltzmann equations. The equations are discretized with Hermite polynomials in velocity space yielding a first order conservation law. A stabilized unsplit perfectly matching layer (PML) formulation is introduced for the resulting nonlinear flow equations. The proposed PML equations exponentially absorb the difference between the nonlinear fluctuation and the prescribed mean flow. We introduce semi-analytic time discretization methods to improve the time step restrictions in small relaxation times. We also introduce a multirate semi-analytic Adams-Bashforth method which preserves efficiency in stiff regimes. Accuracy and performance of the method are tested using distinct cases including isothermal vortex, flow around square cylinder, and wall mounted square cylinder test cases. (C) 2019 Elsevier Inc. All rights reserved.