Investigations of the speed of sound in a cell variable influence in modeling of the flow in a plane channel and flow of the circle cylinder stream of viscous liquid calculating by the method of lattice Boltzmann equations

Анотація

In this work the technique of modeling of two-dimensional flows of viscous liquid by method of lattice Boltzmann equations when sound speed in a cell isn't a fixed value is investigated. Such approach helps to avoid method’s instability and to control the size of a settlement cell, a step on time and Makh number. Ways of setting of some types of boundary conditions are investigated and the new way of setting of a condition of constant pressure is offered. To test proposed algorithm we simulates flow of a viscous liquid in open channel and fluid flow past a circular cylinder. The numerical solutions of the flow in a channel were compared with the corresponding results obtained by the finite element method in the Comsol Multiphysics package. The form of the Karman vortex path after the circular cylinder is shown and it is discussed the dependence between the flow pattern and Reynolds number. To analyze the accuracy of unsteady vortex flows we propose to calculate Strukhal's number in a new way based on the horizontal vortex distance. In the paper there is also investigated the dependence between the numerical result’s accuracy and local Makh number. It is shown that results can be obtained with the relative error less than 10% and the local Makh number should be less than 0.3.