TY - JOUR

T1 - Simulation of Shock Waves in Methane: A Self-Consistent Continuum Approach Enhanced Using Machine Learning

AU - Максудова, Зарина Маратовна

AU - Шакурова, Лия Алимджановна

AU - Кустова, Елена Владимировна

PY - 2024/9/20

Y1 - 2024/9/20

N2 - 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 CH4 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.

AB - 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 CH4 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.

KW - bulk viscosity

KW - computational fluid dynamics

KW - machine learning

KW - mathematical modeling

KW - methane

KW - neural networks

KW - shock waves

KW - vibrational excitation

UR - https://www.mendeley.com/catalogue/40352a17-78f1-3041-91e8-08c8c71ad1e4/

U2 - 10.3390/math12182924

DO - 10.3390/math12182924

M3 - Article

VL - 12

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 18

M1 - 2924

ER -