A preconditioned lattice Boltzmann flux solver for steady flows on unstructured hexahedral grids. (English) Zbl 1521.76707
Summary: The lattice Boltzmann flux solver (LBFS), first introduced by C. Shu et al. [“Development of lattice Boltzmann flux solver for simulation of incompressible flows”, Adv. Appl. Math. Mech. 6, No. 4, 436–460 (2014; doi:10.4208/aamm.2014.4.s2)] on structured meshes, allows fluid flow problems to be solved on unstructured meshes discretised by the finite volume method. The solver calculates the macroscopic fluxes at the cell interfaces from a local reconstruction of the lattice Boltzmann solution. In this paper the LBFS is extended to three-dimensional unstructured hexahedral meshes and a preconditioned lattice Boltzmann flux solver (PLBFS) is presented. The PLBFS involves applying the preconditioning technique proposed by Z. Guo et al. [“Preconditioned lattice-Boltzmann method for steady flows”, Phys. Rev. E (3) 70, No. 6, Article ID 066706, 8 p. (2004; doi:10.1103/PhysRevE.70.066706)]) to the LBFS and is achieved by modifying the equilibrium distribution function used to calculate the macroscopic fluxes at the cell interface. When the PLBFS is applied to steady flow problems, it is shown that convergence is significantly accelerated and the accuracy of predictions with unstructured grids is greatly improved when compared to the LBFS. This paper also introduces a strategy for choosing the optimal value of preconditioning factor with unstructured hexahedral meshes.
MSC:
| 76M28 | Particle methods and lattice-gas methods |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
lattice Boltzmann flux solver; unstructured grids; preconditioning; steady flows; acceleration of convergenceReferences:
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