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Entropy 2015, 17(11), 7713-7735;

From Lattice Boltzmann Method to Lattice Boltzmann Flux Solver

Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Street, Nanjing 210016, China
Author to whom correspondence should be addressed.
Academic Editors: Sauro Succi and Ignazio Licata
Received: 10 September 2015 / Revised: 19 October 2015 / Accepted: 2 November 2015 / Published: 13 November 2015
(This article belongs to the Special Issue Non-Linear Lattice)
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Based on the lattice Boltzmann method (LBM), the lattice Boltzmann flux solver (LBFS), which combines the advantages of conventional Navier–Stokes solvers and lattice Boltzmann solvers, was proposed recently. Specifically, LBFS applies the finite volume method to solve the macroscopic governing equations which provide solutions for macroscopic flow variables at cell centers. In the meantime, numerical fluxes at each cell interface are evaluated by local reconstruction of LBM solution. In other words, in LBFS, LBM is only locally applied at the cell interface for one streaming step. This is quite different from the conventional LBM, which is globally applied in the whole flow domain. This paper shows three different versions of LBFS respectively for isothermal, thermal and compressible flows and their relationships with the standard LBM. In particular, the performance of isothermal LBFS in terms of accuracy, efficiency and stability is investigated by comparing it with the standard LBM. The thermal LBFS is simplified by using the D2Q4 lattice velocity model and its performance is examined by its application to simulate natural convection with high Rayleigh numbers. It is demonstrated that the compressible LBFS can be effectively used to simulate both inviscid and viscous flows by incorporating non-equilibrium effects into the process for inviscid flux reconstruction. Several numerical examples, including lid-driven cavity flow, natural convection in a square cavity at Rayleigh numbers of 107 and 108 and transonic flow around a staggered-biplane configuration, are tested on structured or unstructured grids to examine the performance of three LBFS versions. Good agreements have been achieved with the published data, which validates the capability of LBFS in simulating a variety of flow problems. View Full-Text
Keywords: lattice Boltzmann flux solver; Navier–Stokes equation; lattice Boltzmann equation; incompressible flow; compressible flow lattice Boltzmann flux solver; Navier–Stokes equation; lattice Boltzmann equation; incompressible flow; compressible flow

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Wang, Y.; Yang, L.; Shu, C. From Lattice Boltzmann Method to Lattice Boltzmann Flux Solver. Entropy 2015, 17, 7713-7735.

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