浸入运动边界-格子Boltzmann方法4种固含率计算方法对比研究

A comparative study of four solid ratio calculation methods for immersed moving boundary-lattice Boltzmann method

为了达到流固耦合,格子Boltzmann方法(LBM)可采用浸入运动边界法(IMB)实现移动颗粒边界上的无滑移条件.该耦合方式(IMB-LBM)中固含率计算方法对流固耦合计算精度和效率有影响.对常用的固含率4种计算方法,即蒙特卡洛法(MCM)、单元分解法(UDM)、近似多边形法(APM)和闭合边界法(CBM),分别阐述其具体算法,对比了它们的计算精度和计算效率;最后通过圆盘颗粒非连续变形分析方法(DDDA)与IMB-LBM耦合模型下的一个多颗粒沉降流固耦合算例,对比分析了它们在流固耦合计算过程中的耗时.结果表明:1)CBM无误差,MCM和UDM在随机点数取1000,子单元数取100时误差稳定在1%以下,APM在颗粒直径大于格子长度10倍时,误差小于0.44%;2)MCM和UDM的计算精度及耗时分别与随机点数和子单元数相关,它们的计算耗时大于APM和CBM;3)计算效率上,APM>CBM>UDM>MCM,其中CBM计算耗时略微大于APM,APM和UDM计算耗时分别比MCM少2个和1个数量级.该结果可为IMB-LBM耦合模型中固含率计算方法优选提供借鉴.

The immersed moving boundary(IMB)can be implemented into the lattice Boltzmann method(LBM)to guarantee non-slip condition at moving particle boundaries,in which fluid-solid coupling can be realized.This IMB-LBM coupled model requires calculating the solid ratio.The calculation method of solid ratio has an effect on the accuracy and efficiency of fluid-solid coupling calculation.Four common methods for calculating solid ratio are Monte Carlo method(MCM),unit decomposition method(UDM),approximate polygon method(APM)and closed boundary method(CBM).In this paper,the specific algorithms of the four methods are described and their calculation accuracy and efficiency are compared.And their time consumption in fluid-solid coupling calculation is compared through modeling a multi-particle settlement fluid-solid coupling example by disk discontinuous deformation analysis(DDDA)and lattice Boltzmann method(LBM)coupling model.The results reveal that:1)CBM has no error,while the relative error of MCM and UDM is about 1%when the number of random points is 1000 and the number of sub-units is 100.The error of APM is less than 0.44%when the particle diameter is 10 times larger than the lattice length;2)The accuracy and time consumption of MCM and UDM are respectively correlated with the number of random points and sub-units,and their calculations are more time-consuming than both APM and CBM;3)In calculation efficiency,APM>CBM>UDM>MCM,the time consumption of CBM is a little more than APM,and the time consumption of a single calculation in MCM is 2 orders of magnitude more than that of APM.The time consumption of a single calculation in MCM is 1 orders of magnitude more than that of UDM.These conclusions can provide a reference for the optimization of the calculation method of solid ratio in IMB-LBM coupled model.