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Meshfree lattice Boltzmann flux solver for compressible inviscid flows
Author(s) -
Zhan Ningyu,
Chen Rongqian,
Liu Jiaqi,
Qiu Ruofan,
You Yancheng
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4933
Subject(s) - lattice boltzmann methods , inviscid flow , solver , discretization , mathematics , riemann solver , mathematical analysis , geometry , mechanics , physics , mathematical optimization , finite volume method
Abstract In this work, a meshfree Lattice Boltzmann Flux Solver (LBFS) is proposed to resolve compressible flow problems based on scattered points without mesh connections. The new method employs the Least Square‐based Finite Difference (LSFD) scheme to discretize the governing equations. In order to simulate discontinuous problems such as shock wave, the mid‐point between two adjacent nodes is regarded as a discontinuous interface over which the Riemann problem is established. The local fluxes at this interface point are reconstructed by LBFS using the local solution of the Lattice Boltzmann Equation (LBE) as well as its correlations to macroscopic variables and moment relations. The LBFS is constructed based on the non‐free parameter D1Q4 model: the normal component of the particle velocity on the interface is retained, while the tangential component is reconstructed by the macroscopic variables on both sides of the interface. The meshfree LBFS expects some intriguing merits. On one hand, it inherits the physical robustness of the LBFS: the local fluxes are reconstructed from the physical solutions instead of mathematical interpolations. On the other hand, it allows the implementation at arbitrarily distributed nodes, which credits to the flexibility of the method. Representative examples of compressible flows, including Sod shock tube, Osher‐Shu shock tube, flow around NACA0012 airfoil, flow around staggered NACA0012 biplane configuration and shock reflection problem, are simulated by the proposed method for comprehensive evaluation of the meshfree LBFS.