MODIFIED METHOD OF LATTICE BOLTZMANN EQUATIONS WITH IRREGULAR MESH

Abstract

A modified mathematical method of lattice Boltzmann equations is offered. The offered method may be used for numerical modeling of fluid motion, based on finite elements of irregular space structure. It is suggested to get rid of the requirements of lattice repetition and symmetry which are used in the traditional method of the lattice Boltzmann equations. In the case of irregular mesh the discrete set of allowed speeds is determined by the geometry of finite volumes which surround the current finite volume, and will appear unique for every node. The process of their determination can be performed once before the beginning of modeling and repeated in the case of correction of structure of calculation mesh. For determination of stakes of the moved masses it is suggested to calculate the values of expressions which present the probabilities of the given particle transfers during one tick of the calculation time by integration of distribution functions with the proper window functions which represent geometrical problem specifications.