Computer simulation of gas-dynamic processes: a one-dimensional approach

Abstract

The relevance of this work derives from the need for effective information technologies and software tools for modeling gas-dynamic processes in technical systems. Under modern conditions, the use of full-scale multidimensional models is associated with significant computational costs and complexity of software implementation, which limits their application in practical problems. In this context, one-dimensional models gain particular importance as a basis for developing optimized numerical solution algorithms that provide a reasonable balance between accuracy, computational efficiency, and implementation complexity. The objective of the study is to develop a one-dimensional mathematical model and a software package for numerical simulation of thermogasdynamic processes in flow elements of technical systems, as well as to verify and analyze the accuracy of the developed model. The aim of the study is to develop, implement, and verify a unified method for investigating gas-dynamic processes based on one-dimensional mathematical modeling using modern numerical analysis techniques. Special attention is paid to the development of efficient computational algorithms that take into account key physical processes (gas flow, heat and mass transfer, energy transformations, turbulence, and hydraulic losses), as well as ensure stability, convergence, and computational efficiency in software implementation. The object of the study is the processes of numerical modeling of gas-dynamic phenomena in flow elements of technical systems (pipelines, channels, heat exchangers, piston units), which are characterized by unsteady behavior, wave effects, and intensive heat and mass transfer processes. The subject of the study is methods based on a generalized one-dimensional mathematical model for calculating gas-dynamic processes in flow elements of technical systems. The results of the study showed that methods for improving numerical stability and reducing computational errors have been investigated and implemented, which ensured stable operation of algorithms in modeling unsteady gas-dynamic processes. The developed model is implemented as a software package designed for computational experiments and further analysis of simulation results. The performed verification, based on comparison with known analytical, numerical, and experimental data, confirmed the correctness, accuracy, and efficiency of the proposed algorithms. The conclusion confirms the feasibility of using one-dimensional computational models as an effective tool for computer modeling of complex physical processes. The proposed approach can be applied in the development of modern information technologies and in further scientific research in the field of gas dynamics and thermophysics, while the relative error does not exceed 5%.