Numerical simulation of incompressible viscous external flow using mesh-free lattice Boltzmann method

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In recent years, the lattice Boltzmann method (LBM) has become an alternative and promising computational fluid dynamics approach for simulation of complex fluid flows. Despite its huge success in many practical applications, the conventional (standard) LBM is restricted to the lattice uniformity in the physical space. This is an important drawback of the standard LBM for the application to flow problems with complex geometry. Currently there are several ways to remove this drawback of standard LBM. One of these methods is the Taylor series expansion and least squares-based LBM (TLLBM).This method is based on the standard LBM with introduction of the Taylor series expansion and the least squares approach. The salient feature of the TLLBM is the fact that the final equation is an explicit form and essentially has no limitation on the mesh structure and lattice model. In the present work, the TLLBM with D2Q9 lattice model is used to simulate 2-D steady incompressible viscous external flow on non-uniform meshes.Two test cases are studied: a) flow past a circular cylinder with a non-uniform O-type mesh; b) flow past a NACA0012 airfoil at different attack angles with orthogonal and non-uniform C-type mesh. It was found that this method can give very accurate results.

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Journal of Solid and Fluid Mechanics
Volume 4, Issue 4 - Serial Number 4
May and June 2015
Pages 175-189

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