燃烧模拟的多相多材料统一公式
A unified multi-phase and multi-material formulation for combustion modelling
摘要：
这项工作的动机是产生一个完整的配方，由于爆轰波加载的材料响应。在这里，我们专注于弹塑性结构响应。特别是，我们感兴趣的是捕获混溶和不混溶的行为内凝聚相炸药所产生的共存的反应性载体混合物的混溶材料，和几个材料界面，由于不混溶的杂质，如颗粒或空腔的存在。炸药的动力学和热力学演化通过它们的共享界面传递到一个或多个惰性限制器，这些惰性限制器可能经历严重的拓扑变化。我们还希望考虑限制器的弹性和塑性结构响应，而不是对其行为进行流体动力学假设。这些作者以前的工作已经满足了这些要求，通过同时解决适当的方程组的行为的凝聚相炸药和弹塑性行为的约束。在目前的工作中，我们采用了一个单一的系统的偏微分方程（PDE）提出的Peshkov和Romenski，这是能够占不同状态的物质通过概括的概念的失真张量超越固体。我们合并，制定一个单一的系统的PDE，满足共存的可混溶和不可混溶的爆炸混合物的要求。我们提出的数学推导和构造适当的算法，其解决方案。所得到的模型进行了验证，对几个用例的精确解，包括机械和热引起的，无粘和粘性爆炸。结果表明，该模型可以准确地模拟非常广泛的问题，涉及反应和惰性材料之间的非线性相互作用在一个单一的框架。
英文摘要：
The motivation of this work is to produce an integrated formulation for material response due to detonation wave loading. Here, we focus on elastoplastic structural response. In particular, we are interested to capture miscible and immiscible behaviour within condensed-phase explosives arising from the co-existence of a reactive carrier mixture of miscible materials, and several material interfaces due to the presence of immiscible impurities such as particles or cavities. The dynamic and thermodynamic evolution of the explosive is communicated to one or more inert confiners through their shared interfaces, which may undergo severe topological change. We also wish to consider elastic and plastic structural response of the confiners, rather than make a hydrodynamic assumption for their behaviour. Previous work by these authors has met these requirements by means of the simultaneous solution of appropriate systems of equations for the behaviour of the condensed-phase explosive and the elastoplastic behaviour of the confiners. In the present work, we employ a single system of partial differential equations (PDEs) proposed by Peshkov and Romenski, which is able to account for different states of matter by means of generalising the concept of distortion tensors beyond solids. We amalgamate that formulation with a single system of PDEs which meets the requirement of co-existing miscible and immiscible explosive mixtures. We present the mathematical derivation and construct appropriate algorithms for its solution. The resulting model is validated against exact solutions for several use-cases, including mechanically- and thermally-induced, inviscid and viscous detonations. Results indicate that the model can accurately simulate a very broad range of problems involving the nonlinear interaction between reactive and inert materials within a single framework.
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