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

• Published in: Computers & fluids 2015-08, Vol.116, p.46-59
• Main Authors: David, Damien, Kuznik, Frederic, Johannes, Kevyn, Merlier, Lucie
• Format: Article
• Language: English
• Subjects: Accuracy; Axis-symmetric flows; Boundary conditions; Computer simulation; Consistency; Engineering Sciences; Errors; Lattice Boltzmann models; Lattices; Mathematical models; Mechanics; Thermics; Truncation error analysis; Truncation errors
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2015.04.010

•In, Guo’s model for axis-symmetric flows, the moments are multiples of the radius.•A rigorous Taylor series analysis is applied on the discrete model to validate consistency.•The truncation error highlights second order accuracy and a spurious term.•A new axis boundary condition is presented.•The new boundary condition improves greatly the precision of the model. This paper is the continuity of Guo’s work (2009) 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 ur/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.