Linear lattice Boltzmann schemes for acoustic: Parameter choices and isotropy properties

  • Authors:

  • Adeline Augier;FrançOis Dubois;LoïC Gouarin;Benjamin Graille

  • Affiliations:

  • Université Paris-Sud, Laboratoire de Mathématiques, UMR 8628, Orsay, F-91405, France;Université Paris-Sud, Laboratoire de Mathématiques, UMR 8628, Orsay, F-91405, France and Conservatoire National des Arts et Métiers, Department of Mathematics, Paris, France;Université Paris-Sud, Laboratoire de Mathématiques, UMR 8628, Orsay, F-91405, France;Université Paris-Sud, Laboratoire de Mathématiques, UMR 8628, Orsay, F-91405, France

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2013

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Abstract

In this paper we investigate the numerous possible parameter choices for linear lattice Boltzmann schemes according to the definition of the order of isotropy given in Augier et al. (in press) [4]. This property-written in a general framework that includes all of the D"dQ"q schemes-can be understood through a group operation. The resulting relationships between the parameters of the scheme (defining the equilibrium states and relaxation times) yield a rigorous methodology that should be followed if one is to ensure isotropy at a given order. For acoustic applications in two spacial dimensions (namely D"2Q"9 and D"2Q"1"3 schemes) this methodology is used to propose a full description of the sets of parameters that are isotropic at order m (m@?{1,2,3,4,5} for D"2Q"9 and m@?{1,2} for D"2Q"1"3). We include numerical illustrations for the D"2Q"9 scheme obtained with the code LBMpy developed in the laboratory of Mathematics of the University Paris-Sud.