An improved axisymmetric lattice Boltzmann flux solver for axisymmetric isothermal/thermal flows. (27th May 2019)

• Record Type: Journal Article
• Authors: Zhang, Liangqi; Chen, Zhen; Yang, Liming; Zhang, Mengqi
• Is Part Of: International journal for numerical methods in fluids. Volume 90:Number 12(2019)
• Page Start: 632
• Page End: 650
• Publication Date: 2019-05-27
• Subjects: axisymmetric flows -- finite volume method -- flux evaluation -- lattice Boltzmann method; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4738
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: In this work, an improved axisymmetric lattice Boltzmann flux solver (LBFS) is proposed for simulation of axisymmetric isothermal and thermal flows. This solver globally resolves the axisymmetric Navier‐Stokes (N‐S) equations through the finite volume strategy and locally reconstructs numerical fluxes with solutions to the lattice Boltzmann equation. Compared with previous axisymmetric LBFS, some novel strategies are adopted in this work to simplify the formulations and improve the accuracy. First, the macroscopic equations are reformulated to reduce the number of source terms and remove spatial derivatives involved in the source terms. Second, the local reconstruction of numerical fluxes utilizes relationships given by the Chapman‐Enskog analysis and combines the radial coordinate ( r ) with the local solution to the standard LB equation. By adopting these two modifications, the present axisymmetric LBFS avoids the fractional‐step formulation and the finite‐difference approximation adopted in the previous solver, which reduces the complexity of implementation. Moreover, an alternative way of predicting intermediate pressure is proposed, which could effectively fix the inaccurate resolution of the pressure field in previous axisymmetric LBFS. Further extensions are made to enrich the applicability of the present solver in thermal axisymmetric flows. Validations on various benchmark tests are carried out for comprehensive evaluation of the robustness and flexibility of the proposed solver. Abstract : An improved axisymmetric lattice Boltzmann flux solver (LBFS) is proposed for simulation of axisymmetric isothermal and thermal flows. With some novel strategies, the proposed axisymmetric LBFS become more compact than the previous solver by avoiding both the fractional‐step procedure and the finite‐difference approximations in the previous solver, which facilitates the implementation. Moreover, an alternative pressure approximation is proposed in the present solver, which makes the predicted pressure field more accurate than the previous solver.