Simulation of continuous flows with discrete models

Abstract

The vast majority of heat and power processes include the motion of significant amounts of gases and liq-uids. This makes it important and quite urgent to develop approaches for computer simulation and visualiza-tion of continuum flows in technological devices and pipelines. A whole set of new approaches to mathematical modelling of continuum flows has been recently developed. The most common one is using discrete mathematical models for these purposes. Discrete approaches can simplify modeling procedures in cases where traditional methods require complex time-consuming calculations. At the same time, correct-ness of description of various flow regimes by the discrete methods is often questioned. The second problem of the mentioned models is a large-scale transition from model discrete parameters to generally accepted macroscopic characteristics of flows. The purpose of this work is to determine continuous flow regimes that can be correctly described by certain models. The paper considers discrete dynamic models in the form of lattice gases. A continuum in this case is represented by a set of particles moving only in allowed directions. Despite certain limitations, there is solid evidence that lattice gases quite successfully describe a whole range of hydrodynamic phenomena, and the obtained results do not contradict the generally accepted views on the physical nature of continuum motion processes. The paper describes approaches that allow estimating flow parameters using generally accepted macroscopic indicators. It also studies possible application areas of lattice gas models using the motion of virtual particles on a spatial lattice (HPP and FHP models) and the model based on the discrete analogue of the Boltzmann equation (LBM model) to simulate and visualize continuum flows. The obtained data are in good agreement with the generally accepted results and do not contradict the provisions of classical hydrodynamics. The paper shows that the models considering particle collisions (HPP and FHP) are applicable to describing gas flows in laminar regimes. The LBM model should be considered to be more correct for simulation and visualization of real fluid flows.