The direct numerical simulation of blast waves is a challenging task due to the wide range of spatial and temporal scales involved. Moreover, in a real environment (topography, urban area), the blast wave interacts with geometrical obstacles, resulting in reflection, diffraction, and wave recombination phenomena. The shape of the front becomes complex, which limits the efficiency of simple empirical methods. This work aims at contributing to the development of a fast running method for blast waves propagating in the presence of obstacles. This is achieved through an ad hoc extension of the simplified hyperbolic geometrical shock dynamics (GSD) model, which leads to a drastic reduction in the computational cost in comparison with the full Euler system. The new model, called geometrical blast dynamics, is able to take into account any kind of source and obstacle. It relies on a previous extension of GSD for diffraction over wedges to obtain consistent physical behavior, especially in the limit of low Mach numbers. The new model is fully described. Its numerical integration is straightforward. Results compare favorably with experiments, semiempirical models from the literature, and Eulerian simulations, over a wide range of configurations.

中文翻译：

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爆炸波传播几何冲击动力学的扩展

由于涉及广泛的空间和时间尺度，冲击波的直接数值模拟是一项具有挑战性的任务。此外，在真实环境（地形、市区）中，冲击波与几何障碍物相互作用，导致反射、衍射和波复合现象。锋面的形状变得复杂，这限制了简单经验方法的效率。这项工作旨在为开发一种在存在障碍物的情况下传播冲击波的快速运行方法做出贡献。这是通过简化双曲几何冲击动力学 (GSD) 模型的临时扩展来实现的，与完整的欧拉系统相比，这导致计算成本大幅降低。新模型，称为几何爆炸动力学，能够考虑任何类型的来源和障碍。它依赖于 GSD 的先前扩展，用于楔形衍射以获得一致的物理行为，尤其是在低马赫数的限制下。对新模型进行了全面描述。它的数值积分很简单。结果与实验、文献中的半经验模型和欧拉模拟在广泛的配置范围内相比具有优势。