Abstract An accurate shock- and interface-capturing method is introduced for simulations of compressible multiphase flows. First, an associated Godunov-type numerical scheme is established for a five-equation two-phase model obtained from a seven-equation model by assuming a single velocity and a single pressure between two phases. The computational finite-volume Riemann solver using the scheme and computing algorithms is presented. Next, an interface-sharpening technique (IST) is extended for the compressible two-phase model to improve numerical simulations and correct diffusion errors. The modified IST was applied as postprocessing to correct the numerical diffusion error in the solution of the discretization scheme while maintaining a sharp interface with a desired thickness after each time step. A mixture-consistent interface regularization approach of all conservative variables is combined with the IST to obtain consistent thermodynamic laws for the mixture, ensuring the consistency of the variables in the correction process. Several examples of fluid interface simulations including shock-tube, shock-bubble interactions, and underwater explosions were performed to demonstrate the accuracy and capability of the proposed method. Those compressible multiphase flow problems are complicated by the presence of both shock waves and the dynamics of interfaces. Comparisons of the numerical method with theoretical results and experimental data indicate that the present method can simulate interface dynamics with the presence of shock waves and large density differences.

中文翻译：

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使用界面锐化五方程模型对存在冲击波的多相可压缩流进行数值模拟

摘要 引入了一种精确的冲击和界面捕获方法来模拟可压缩多相流。首先，通过假设两相之间的单一速度和单一压力，为从七方程模型获得的五方程两相模型建立了相关的 Godunov 型数值方案。提出了使用该方案和计算算法的计算有限体积黎曼求解器。接下来，将界面锐化技术 (IST) 扩展到可压缩两相模型，以改进数值模拟和校正扩散误差。修改后的 IST 被用作后处理，以校正离散化方案解中的数值扩散误差，同时在每个时间步长后保持具有所需厚度的清晰界面。所有保守变量的混合物一致界面正则化方法与IST相结合，以获得混合物的一致热力学定律，确保校正过程中变量的一致性。流体界面模拟的几个例子包括激波管、激波气泡相互作用和水下爆炸，以证明所提出方法的准确性和能力。由于冲击波和界面动力学的存在，这些可压缩的多相流问题变得复杂。数值方法与理论结果和实验数据的比较表明，本方法可以模拟存在冲击波和大密度差异的界面动力学。