Abstract In this paper, we propose an arbitrary Lagrangian Eulerian (ALE) method for solving compressible multi-material flows on two-dimensional adaptive unstructured triangular meshes. We couple a conservative equation related to a γ-model (or a mass fractional model) with the system of fluid equations for obtaining the specific heat ratio of the multi-material flows. The discretization of the coupling system is implemented by Runge-Kutta Discontinuous Galerkin (RKDG) method and the vertex velocity is obtained by the variational approach. The new meshes can be automatically redistributed and concentrated on regions with large gradient values. This work is a new development of our previous research for solving single-material flow with ALE-RKDG method. The proposed method is more concise compared to many other methods and robust for the simulations of multi-material flows. Numerical examples are presented to verify this method, and the results show that our scheme is not only efficient but also with the anticipative accuracy.

中文翻译：

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自适应非结构​​网格上多材料流动的任意拉格朗日-欧拉 RKDG 方法

摘要 在本文中，我们提出了一种任意拉格朗日欧拉 (ALE) 方法，用于求解二维自适应非结构​​三角形网格上的可压缩多材料流动。我们将与 γ 模型（或质量分数模型）相关的保守方程与流体方程系统耦合，以获得多材料流的比热比。耦合系统的离散化采用Runge-Kutta Discontinuous Galerkin(RKDG)方法实现，顶点速度采用变分法求得。新网格可以自动重新分布并集中在具有大梯度值的区域。这项工作是我们以前用 ALE-RKDG 方法解决单一材料流动的研究的新进展。与许多其他方法相比，所提出的方法更简洁，并且对于多材料流动的模拟具有鲁棒性。给出了数值例子来验证该方法，结果表明我们的方案不仅有效而且具有预期的准确性。