A finite-difference lattice Boltzmann model with second-order accuracy of time and space for incompressible flow

In this paper, a kind of finite-difference lattice Boltzmann method with the second-order accuracy of time and space (T2S2-FDLBM) is proposed. In this method, a new simplified two-stage fourth order time-accurate discretization approach is applied to construct time marching scheme, and the spatial g...

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Bibliographic Details
Published in:arXiv.org 2019-11
Main Authors: Chen, Xinmeng, Chai, Zhenhua, Wang, Huili, Shi, Baochang
Format: Article
Language:English
Subjects:
Accuracy
Computational fluid dynamics
Computer simulation
Discretization
Finite difference method
Fluid flow
Incompressible flow
Mathematical analysis
Model accuracy
Stability analysis
Time marching
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Summary:In this paper, a kind of finite-difference lattice Boltzmann method with the second-order accuracy of time and space (T2S2-FDLBM) is proposed. In this method, a new simplified two-stage fourth order time-accurate discretization approach is applied to construct time marching scheme, and the spatial gradient operator is discretized by a mixed difference scheme to maintain a second-order accuracy both in time and space. It is shown that the previous finite-difference lattice Boltzmann method (FDLBM) proposed by Guo [1] is a special case of the T2S2-FDLBM. Through the von Neumann analysis, the stability of the method is analyzed and two specific T2S2-FDLBMs are discussed. The two T2S2-FDLBMs are applied to simulate some incompressible flows with the non-uniform grids. Compared with the previous FDLBM and SLBM, the T2S2-FDLBM is more accurate and more stable. The value of the Courant-Friedrichs-Lewy condition number in our method can be up to 0.9, which also significantly improves the computational efficiency.
ISSN:2331-8422