Research On The Local Refinement Implementation Of Rectangular Grids Based On Lattice Boltzmann Method With Multiple Relaxation Model

The lattice Boltzmann method is different from the traditional numerical simulation method,it based on molecular kinetic theory,the mesoscopic scale reflects the physical essence of fluid flow,compared with the traditional simulation method,control equation for discrete algebraic equations,with the characteristics of the second order accuracy,fast convergence speed,easy to realize large-scale parallel computing,for different flow boundary,the boundary condition processing is simple,the program is easy to implement,available for more than 20 years,the theory research,the model and algorithm,the experiment has achieved prominent progress,It has been widely used in nano-thermal fluid,porous medium,magnetic fluid,multiphase flow,and other fields.This paper focuses on the Boltzmann method of locally encrypted lattice for rectangular grids.The main research content is the use of multi-relaxation(MRT)model to achieve the independent transfer of momentum,energy,and mass and the continuous transfer of space moment between different mesh densities.The algorithm flow of rectangular mesh local encryption is established,the encryption program is written,and the corresponding cavity flow is solved for encryption.Firstly,the multi-relaxation model adopts multiple independent relaxation parameters in the moment space,decomposes the relaxation process of particles into relatively independent processes in multiple directions,and transfers the space moments such as energy,momentum and mass independently,improving the accuracy and stability of the calculation and more consistent with the physical nature of flow.Secondly,in the flow field,there are often some regions with large physical quantity changes,and the uniform grid will often produce large errors,leading to spatial oscillation,numerical instability,and reduced convergence speed.In order to improve the accuracy of the calculation,the mesh needs to be encrypted in the above areas,so as to ensure the smooth change of physical quantity and improve the stability of the calculation.In the region where the change of a physical quantity is relatively gentle,the coarse grid can often meet the requirement of precision.In the process of mesh encryption,data at some points can't be directly transferred from other grid points.In this paper,the Lagrange interpolation method is used to calculate the values at the interpolation points,and the continuity of macroscopic physical quantities such as density,velocity,and stress on the grid interface is guaranteed.In this paper,the rectangular mesh model D2Q9 is adopted and the classical square cavity flow example is used to verify the effectiveness of local mesh encryption.In a square cavity flow,mobile roof in the Angle of two huge quantity change,lead to stress discontinuity,this article for grid refinement of this area,and the calculation results of the steady flow field under different grid density are compared,the results show that encryption area calculation error is decreased obviously,the noise dropped significantly,in the area of stress changes drastically to capture the stress changes in the details,the results correspond with the classic example,confirmed the correctness of the local grid refinement method.