Optimization Discrete Unified Gas Kinetics Scheme For Three-Dimensional Flows

In recent years,numerical methods for multiscale flows have attracted a lot of attention in the fields of energy,environment,and defense.Since multiscale flow problems usually span multiple spatial and temporal scales,they cannot be solved by traditional fluid dynamics theories and methods.The discrete unified gas kinetic scheme(DUGKS)based on kinetic theory and lattice Boltzmann method is suitable for hydrodynamic simulations in all watersheds.However,for the simulation of three-dimensional flow,the spatial reconstruction algorithm of DUGKS micro-flux is complicated,the time step is limited by the smaller Courant-Friederichs-Lewy(CFL)number(CFL<1),and the numerical dissipation is large.Based on DUGKS,this paper puts forward a new micro-flux reconstruction method,optimizes the algorithm structure,relaxes the stability conditions,develops an efficient three-dimensional DUGKS algorithm,and studies the computational efficiency,numerical accuracy and stability of the algorithm.The main work is as follows:In this paper,the DUGKS optimization algorithm for three-dimensional flow is developed by combining the idea of staggered grid.Firstly,based on isothermal Boltzmann-BGK equation and nonisothermal double distribution Boltzmann equation,the evolution equation of distribution function at the control center is established by finite volume method,and the evolution equation of distribution function at the grid point is established by integrating along the characteristic line.A new solution method of micro-flux reconstruction is proposed by replacing the original midpoint rule with trapezoidal rule,so as to develop DUGKS optimization algorithm.Then,the new algorithm is compared with the original DUGKS from the aspects of algorithm structure,numerical accuracy,numerical stability and computational efficiency.Further,based on DUGKS optimization algorithm,the turbulent Taylor-Green vortex and threedimensional square cavity natural convection are numerically studied respectively.By numerical calculation,the numerical performances of the original DUGKS method and the optimization method are compared under different grid sizes and time steps.The numerical results show that: Not only the calculation speed is twice as high as that of the original DUGKS in isothermal and non-isothermal flows under the same working conditions.But also the optimized DUGKS is superior to the original algorithm in terms of numerical dissipation and stability,it can still obtain accurate calculation results under sparse grid and large time step(CFL=1.7).the calculation cost is further greatly reduced by using larger spatial grid and time step.The optimized DUGKS has a simple structure and significantly improves the computational efficiency.It overcomes the shortcomings of the original DUGKS with large numerical dissipation and improves numerical accuracy.It breaks the limitation that the CFL number is less than 1 in the previous explicit kinematic format,and improves the numerical stability.