# VISCOUS FLUID FLOW MODELING WITH THE LATTICE BOLTZMANN METHOD ON GRAPHICS PROCESSORS USING WebGL API

### Abstract

This work is dedicated to the modeling methodology of a viscous fluid flows with the lattice Boltzmann method on graphic processors based on the technology of images rendering in web browsers WebGL. A two-dimensional nine-velocity LBM model (D2Q9) with a collision integral in a Bhatnagar-Gross-Kruk approximation form is shown. The possibilities of calculation acceleration using WebGL technology is described, namely features of using textures to contain values of some physical quantities in numerical algorithms and using fremebuffers to storage the textures, influence of the texture parameters on the numerical algorithms, features of shaders programming. The questions of shader programs using for carrying out stages of physical modeling were considered. The proposed methodology was used to develop an original web program for modeling of classical test problems. Simulations of the Poiseuille flow in a plane channel and the flow around a circular cylinder in a plane channel were performed. The obtained results were compared with the results of calculations performed in the original verified modeling program based on the lattice Boltzmann method and in the Comsol Multiphysics package with the finite element method. Comparisons of the values of the velocity magnitude showed the consistency of the obtained results with the data of other numerical experiments. The analysis of computational speed in comparison with modeling using the optimized algorithm of a method with use of the technology of parallel calculations on CPU OpenMP in the original program is carried out. It is shown that the acceleration of calculations depends on the number of cells of the calculation grid. The results of the fluid flow modeling around a circular cylinder at Re = 1000 are demonstrated, which are obtained 30 times faster than with the calculations obtained with optimized lattice Boltzmann method and OpenMP technology.

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