Shock absorption by predicting shock wave behavior with precise computational modeling

Shock waves don’t have to be shocking. Now, thanks to a team at Yokohama National University, these predictors are even better understood.

Published on August 19th in Kam Physics of Fluidsthe researchers detailed how the computational models used to simulate shock wave behavior represent very weak shock waves that differ markedly from both theoretical predictions and physical measurements.

Shock waves consist of pressure released from an object moving at high speed of sound, such as an explosion or a supersonic jet. Weak shocks refer to the same changes in pressure, density, and velocity, but they are much smaller than large waves and approach the speed of sound. However, according to co-author Keichi Katamura of Yokohama National University’s Faculty of Engineering, current computational modeling methods have difficulty accurately representing these extremely weak shock waves.

“Shock waves cause instantaneous compression, which results in an increase in entropy,” said co-author Keichi Katamura of Yokohama National University’s Faculty of Engineering.

Entropy refers to disorder, which appears to contradict expected physical behavior, when a wave is moving. According to Katamura, this disorder is at the peak of shock wave impressions. Traditional computational approaches consider very weak shock waves to be diffusive, but this does not account for the more variable variables of the shock wave, especially as it moves.

“Finite volume methods are commonly used to remove inconsistencies in numerical simulations because they can preserve variables even at shock-related inconsistencies,” Kitamura said. “However, computing shock waves using finite volume methods is not always stable and, under certain conditions, presents challenges due to their heterogeneous nature.”

In an analysis focused on understanding the specific properties of numerically represented shock waves, the researchers found that the final state of a moving shock wave can be classified into three regimes: dispersive, transitional, and thinly captured. It turned out, Katamura said, that continuous numerical simulations automatically adjust the physical parameters of a shock wave to match the calculated entropy.

“This work identified the mechanism of propagated weak shock waves,” said Katamura. “Our findings will bridge the gap in understanding between theoretical and physical weak shock waves, potentially contributing to safer, more economical and more accurate designs of future rockets and supersonic aircraft.”

Gaku Fukushima, a postdoctoral researcher in the Department of Mechanical Engineering at the Université de Sherbrooke in Canada, served as a corresponding author on the paper. At the time of the research, there was a Japan Society for the Promotion of Science Postdoctoral Fellow at Fukushima Yokohama National University.