Study on Regularized Lattice Boltzmann Method for High Reynolds Number and Turbulent Flow Simulations

正規化格子ボルツマン法における高レーノルズ数と乱流の流れのシミュレーションの研究

2015-03-25

2015-03-25

In this work, regularized lattice Boltzmann method (RLBM) was studied as a novel approach for applications in high Reynolds number and turbulent flow simulations. The effectiveness of the method is demonstrated by conducting simulations of two-dimensional lid-driven cavity flow, flow past two-dimensional circular cylinder, two- and three-dimensional homogeneous isotropic turbulence flows, and three-dimensional turbulent flow past circular cylinder. RLBM is a variation of single-relaxation-time lattice Boltzmann method (LBM) in which the collision term is regularized by using Chapman-Enskog expansion to derive the non-equilibrium part of the distribution function. Since the collision term is regularized, unlike the Bhatnagar-Gross-Krook (BGK) collision model, RLBM is more closely related to the multi-relaxation-time LBM (MRT-LBM). The advantages of RLBM over the standard LBM are improved numerical stability while maintaining the collision simplicity and lower memory usage. RLBM algorithm is also as simple as LBM. The flexibility of boundary condition implementations similar to the standard LBM, such as bounce-back boundary condition or non-equilibrium extrapolation boundary conditions. An RLBM code was developed for two- and three-dimensional incompressible flow simulations. The code was also written for parallel implementation using OpenMP. For two-dimensional case, simulations were conducted for the lid-driven cavity flow, flow past two-dimensional circular cylinder, flow past two-dimensional square cylinder in a channel and two-dimensional homogeneous isotropic turbulence. Results from these simulations were compared to the traditional finite difference Navier-Stokes solver, entropic lattice Boltzmann method (ELBM) and pseudospectral (PS) method. For three-dimensional case, simulations of three-dimensional homogeneous isotropic turbulence and turbulent ow past a circular cylinder were conducted. For these cases, the effect of under-resolved mesh was studied and compared to the large-eddy simulation based LBM (LES-LBM). Results from RLBM simulations were found to agree very well with the other mentioned methods. Results from two-dimensional flow simulations for all test cases were found to be in good agreement with the standard LBM, ELBM and PS method if the flow is well resolved. For under-resolved simulations, RLBM produced excellent pressure field without unphysical oscillations. A closer observation of the results showed that some form of artificial viscosity is inherent in RLBM. Although the phenomena itself is not necessarily bad, care must be taken when conducting RLBM simulations. The three-dimensional homogeneous isotropic turbulence simulations were conducted specifically to study the behavior of this artificial viscosity. It can be concluded that for well resolved simulations, the damping effect of artificial viscosity is negligible. For under-resolved simulations, the damping effect was found to filter-out high wave number component of the flow simulations. The effect of the artificial viscosity could be beneficial for turbulence simulations. In most engineering applications, the flow simulations cannot be fully resolved due to computational cost and hardware issues. Therefore, the use of turbulent model or modeling the small eddy effect such as in large-eddy simulation is unavoidable. The artificial viscosity effect inherent in RLBM could be valuable for this type of flow simulations. Since turbulent modeling is empirical, fine tuning the parameters can be tedious, whereas large-eddy simulation such as Smagorinsky subgrid model also contains empirical parameters. RLBM's inherent artificial viscosity can alleviate this problem. With no explicit turbulent model, RLBM simulations for under-resolved flow can be considered as implicit large-eddy simulations. The conclusions of this work are that RLBM significantly improves the numerical stability of the standard LBM, it is a feasible method for high Reynolds number flows or turbulence and it is as efficient as the standard LBM while using less memory.

博士（工学）

京都工芸繊維大学

This thesis explores the possibility of using regularized lattice Boltzmann method as an implicit large-eddy-simulations tool. The detail development of the method and its related variant is provided in details.

14303乙第196号

http://hdl.handle.net/10212/2265

en

ETD

Thesis or Dissertation

Thesis