Knudsen layer theory for high-order lattice Boltzmann modelsL. Szalmás
3. Street Kastelykert, Hatvan 3000, Hungary and Dipartimento di Fisica, Università di Roma "La Sapienza" - Piazzale Aldo Moro 2, 00158 Rome, Italy
received 22 February 2007; accepted in final form 29 August 2007; published October 2007
published online 21 September 2007
A Knudsen layer theory is presented within the framework of a high-order lattice Boltzmann model obtained from the fourth-order Gauss-Hermite quadrature. The Kramers problem is analyzed in detail. We employ a multi-relaxation collision operator which is shown to permit a variable layer width. Computer simulations are performed which give excellent agreement with the theoretical derivations. Good qualitative agreement is achieved with the accurate numerical solution of the Boltzmann equation for hard sphere molecules. Our theoretical result clearly indicates that the lattice Boltzmann models with high symmetric velocity sets naturally develop to physically relevant Knudsen layers due to the discrete ordinate origin of the method.
47.11.-j - Computational methods in fluid dynamics.
47.45.-n - Rarefied gas dynamics.
05.20.Dd - Kinetic theory.
© Europhysics Letters Association 2007