Numerical analysis of truncation error, consistency, and axis boundary condition for axis-symmetric flow simulations via the radius weighted lattice Boltzmann model

Damien David (1) , Frederic Kuznik (1) , Kevyn Johannes (1) , Lucie Merlier (1)

1 CETHIL - Centre d'Energétique et de Thermique de Lyon

This paper is the continuity of Guo's work [Phys.Rev., 2009, 046708] about a lattice Boltzmann model for axis-symmetric flows. This is a radius weighted LBM model: all the moments are proportional to the radial coordinate r. A Taylor series analysis is performed on the discrete Boltzmann Model in order to assess the consistency. The truncation error terms do not indicate any error increase along the radial direction, but they contain a spurious term u r /r which considerably reduces the model accuracy when radial velocity is non-null: simulation results highlight a reductions of the order of accuracy (from second to first). A new axis boundary condition was created to improve the model accuracy and to cope with the spurious error term. It was assessed though several test cases.

Mots clés: Lattice Boltzmann models; Axis-symmetric flows; Truncation Error Analysis; Boundary conditions

Domaines: Thermique [physics.class-ph]

Damien David, Frederic Kuznik, Kevyn Johannes, Lucie Merlier. Numerical analysis of truncation error, consistency, and axis boundary condition for axis-symmetric flow simulations via the radius weighted lattice Boltzmann model. Computers and Fluids, 2015, 116, pp.46-59. ⟨10.1016/j.compfluid.2015.04.010⟩. ⟨hal-01287488⟩