The Staggered Discrete Boltzmann Method

Flow is a common form of material movement in nature and engineering,and computational fluid dynamics is the basic method to explore the law of fluid motion.The Discrete Unified Gas Kinetic Scheme(DUGKS)based on Boltzmann equation is an emerging mesoscopic computational fluid Kinetic method.The DUGKS method is not limited by the continuity hypothesis and the semi-empirical constitutive relation,and it is suitable for the flow of any Knudsen number with good mesh flexibility and numerical stability.However,DUGKS needs to calculate the distribution function and balance function for many times in the calculation process and to restore the macroscopic quantity,which results in the low computational efficiency of this method.Based on the DUGKS discrete equation,a new algorithm for solving the discrete Boltzmann model is proposed in this paper,and the new algorithm is applied to the numerical simulation of incompressible fluid.Furthermore,a new gas-solid two-phase flow coupling algorithm is proposed.The main tasks are as follows:Based on the discrete equations of DUGKS using finite volume Staggered grid,this paper proposed a Staggered Discrete Boltzmann Method(SDBM)for incompressible flow.In terms of time,SDBM adopts two-step display format with second-order accuracy to advance and calculates the flow field distribution at half a time step as well as the next moment successively.Spatially,two sets of interlaced grids are used to evolve the distribution functions of the two time points respectively.The numerical simulation results of incompressible fluid using the same discrete equation between SDBM and discrete unified kinetics algorithm show that SDBM has high numerical accuracy and computational efficiency.In this paper,SDBM is further applied to the study of gas-solid two-phase flow coupling algorithm.SDBM and Lagrange method are respectively used to solve the gas-solid two-phase;the interphase interaction is calculated using integral rule and interpolation function to approximate the time and space.On this basis,the SDBM-Lagrange coupling algorithm for gas-solid two-phase flow is proposed.Compared with the classical lattice Boltzmann method,the analysis and calculation results of gas-solid two-phase flow problem show that the proposed algorithm provides a more accurate calculation framework for gas-solid two-phase flow.