Numerical Simulation of the Hydrodynamic and Thermodynamic Characteristics of a Single Sonoluminescence Bubble

Abstract

Single-bubble sonoluminescence (SBSL) arises from the extreme concentration of acoustic energy and its subsequent conversion into light pulses. To track the temporal evolution of this phenomenon, a numerical simulation was conducted to solve the governing non-linear equations using the fourth-order Runge-Kutta algorithm in Mathematica. The mathematical model was developed assuming the preservation of the bubble's perfect spherical shape, and treating the confined gas as a real gas obeying the van der Waals equation. By monitoring the dynamic and thermodynamic variables, it was found that the maximum temperature, , within the gas core reached approximately  at the moment of collapse, coinciding with the reduction of the radius to its minimum value, , of ; these conditions are sufficient to induce gas ionization and plasma formation. Furthermore, the simulation revealed the post-collapse oscillatory behavior of the bubble, characterized by damped rebounds whose amplitudes gradually decay before reaching stability. These results are quantitatively consistent with previous studies, thereby supporting the reliability of the mathematical model in representing the complex non-linear behavior of bubble dynamics under extreme physical conditions