Simulation of Shock Waves in Methane: A Self-Consistent Continuum Approach Enhanced Using Machine Learning

Zarina Maksudova, Liia Shakurova and Elena Kustova ()
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Zarina Maksudova: Department of Mathematics and Mechanics, St. Petersburg University, 7/9 Universitetskaya nab., St. Petersburg 199034, Russia
Liia Shakurova: Department of Mathematics and Mechanics, St. Petersburg University, 7/9 Universitetskaya nab., St. Petersburg 199034, Russia
Elena Kustova: Department of Mathematics and Mechanics, St. Petersburg University, 7/9 Universitetskaya nab., St. Petersburg 199034, Russia

Mathematics, 2024, vol. 12, issue 18, 1-22

Abstract: This study presents a self-consistent one-temperature approach for modeling shock waves in single-component methane. The rigorous mathematical model takes into account the complex structure of CH 4 molecules with multiple vibrational modes and incorporates exact kinetic theory-based transport coefficients, including bulk viscosity. The effects of the bulk viscosity on gas-dynamic variables and transport terms are investigated in detail under varying degree of gas rarefaction. It is demonstrated that neglecting bulk viscosity significantly alters the shock front width and peak values of normal stress and heat flux, with the effect being more evident in denser gases. The study also evaluates limitations in the use of a constant specific heat ratio, revealing that this approach fails to accurately predict post-shock parameters in polyatomic gases, even at moderate Mach numbers. To enhance computational efficiency, a simplified approach based on a reduced vibrational spectrum is assessed. The results indicate that considering only the ground state leads to substantial errors in the fluid-dynamic variables across the shock front. Another approach explored involves the application of machine learning techniques to calculate vibrational energy and specific heat. Among the methods tested, the Feedforward Neural Network (FNN) proves to be the most effective, offering significant acceleration in calculations and providing one of the lowest errors. When integrated into the fluid-dynamic solver, the FNN approach yields nearly a three-fold increase in speed in numerical simulations of the shock wave structure.

Keywords: mathematical modeling; computational fluid dynamics; machine learning; neural networks; methane; shock waves; vibrational excitation; bulk viscosity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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