A well-posed mathematical model of nonisothermal, two-phase, two-velocity flow of a bubbly medium with chemically inert liquid and chemically inert or active gas bubbles is proposed. The model is based on the two-phase Euler equations with the introduction of an additional pressure at the gas-bubble surface, which ensures the well-posedness of the Cauchy problem for a system of governing equations, and the Rayleigh–Plesset equation for radial pulsation of gas bubbles allowing solutions of the soliton type that are realized in experiments to be obtained. The model is validated by comparing calculations of detonation wave propagation with experimental data in water or an aqueous solution of glycerin with bubbles of acetylene–oxygen mixture or with bubbles of argon–hydrogen–oxygen mixture for a volume gas content of 1–6%. The model is shown to provide satisfactory results for the detonation propagation velocity and detonation pressure profiles.

中文翻译：

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气泡液体中冲击波和爆震波的数值模拟

提出了具有化学惰性液体和化学惰性或活性气泡的气泡介质的非等温、两相、双速流动的良定数学模型。该模型基于两相欧拉方程，并在气泡表面引入附加压力，确保控制方程系统的柯西问题的适定性，以及径向的 Rayleigh-Plesset 方程。气泡的脉动允许获得在实验中实现的孤子类型的解决方案。该模型通过将爆震波传播的计算与在水或甘油水溶液中的实验数据进行比较来验证，其中乙炔 - 氧气混合物的气泡或氩 - 氢 - 氧气混合物的气泡，体积气体含量为 1-6%。