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 space structure elements in the neighbourhood of a curvilinear boundary. The fluid movement is described based on the finite element spatial structure, considering the effect of particles’ reflection from solid boundary on the probability distribution function for the directions and speeds of movement. The two approaches of taking into account particles reflection are considered. In the first approach, the construction of the image of the target element in the direction of motion of the particles is done, and then the probability distribution functions of the real finite elements of the computational grid that host the superimposed image are adjusted. The second approach is based on a geometric construction made in the opposite direction, with a corresponding adjustment of the distribution functions for the transfer step. An algorithm of finding probability distribution functions and the force acting on the boundary is considered on an example of solving of the two-dimensional problem.
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