Abstract
The calculation sequence of collision, propagation and macroscopic variables is not very clear in lattice Boltzmann method (LBM) code implementation. According to the definition, three steps should be computed on all nodes respectively, which mean three loops are needed. While the “pull” scheme makes the only one loop possible for coding, this is called semi-implicit scheme in this study. The accuracy and efficiency of semi-implicit scheme are discussed in detail through the simulation of lid-driven cavity flow. Non-equilibrium extrapolation scheme is adopted on the boundary of simulation area. The results are compared with two classic articles, which show that semi-implicit scheme has good agreement with the classic scheme. When Re is less than 3000, the iterations steps of semi-scheme can be decreased by about 30% though comparing the semi-implicit scheme with standard scheme containing three loops. As the Re increases into more than 3400, the standard scheme is not converged. On the contrary, the iterations of semi-implicit scheme are approximately linear to Re.
Highlights
The lattice Boltzmann method has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids
The accuracy and efficiency of semi-implicit scheme is discussed in detail through the simulation of lid-driven cavity flow
The accuracy and efficiency of semi-implicit scheme will be discussed through the simulation of cavity flow
Summary
The lattice Boltzmann method has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. (2015) A Semi-Implicit Scheme of Lattice Boltzmann Method for Two Dimensional Cavity Flow Simulation. The accuracy and efficiency of semi-implicit scheme is discussed in detail through the simulation of lid-driven cavity flow. Lid-driven cavity flow is a well-known fluid flow problem where the fluid is set into motion by a part of containing boundary This type of flow has been used as a benchmark problem for many numerical methods due to its simple geometry and complicated flow behavior.
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