Mie-Grüneisen 型状态方程的松弛法,Physics of Fluids

当前位置： X-MOL 学术 › Phys. fluids › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

Mie-Grüneisen 型状态方程的松弛法
Physics of Fluids ( IF 4.1 ) Pub Date : 2023-11-13 , DOI: 10.1063/5.0169781
Loann Neron _{1,

2} , Richard Saurel _{1,

2} , Alexandre Chiapolino ₁ , François Fraysse ₁

Affiliation

Mie-Grüneisen 型状态方程 (EOS) 广泛用于描述各种物理问题中的固体、液体和气体的热力学，包括凝聚态材料中的冲击波动力学和爆轰波产生的致密气体的热力学行为。Jones–Wilkins–Lee (JWL)、Cochran–Chan 和原始 Mie–Grüneisen EOS 都是相关示例。然而，这些 EOS 存在几个主要困难。首先，它们的有效性范围是有限的，因为这些 EOS 适合参考曲线并且只能容忍与该曲线的微小偏差。第二个困难在于数学公式的复杂性，影响了压力松弛求解器的效率。这两个困难引发了第三个困难。在极端流动条件下，计算失败是很常见的。通常使用“扩展”状态方程的方法来继续计算。例如，低于某个任意密度，JWL EOS 有时会扩展到理想气体 EOS。这项工作提出了一种全新的方法。它包括使用更简单的Noble-Abel-stiffened-gas EOS作为预测器，来关闭相应的流动模型。预测步骤之后是热力学弛豫步骤。借助额外的输运方程，解被投影到目标 EOS 上，在本例中为 Mie-Grüneisen EOS。因此，流动模型是一个扩展版本，对于数值分辨率来说更加有效。该方法通过扩展热力学公式的有效域、使松弛求解器更快、并显着提高计算的鲁棒性，解决了上述三个问题。

"点击查看英文标题和摘要"

Relaxation method for Mie–Grüneisen type equations of state

Mie–Grüneisen type equations of state (EOS) are widely used to describe the thermodynamics of solids, liquids, and gases in a variety of physics problems, including shock wave dynamics in condensed materials and the thermodynamic behavior of dense gases generated by detonation waves. The Jones–Wilkins–Lee (JWL), Cochran–Chan, and original Mie–Grüneisen EOSs are relevant examples. However, these EOSs present several major difficulties. First, their range of validity is limited because these EOSs are fitted to a reference curve and tolerate only small deviations from that curve. The second difficulty lies in the complexity of the mathematical formulations, affecting the efficiency of pressure relaxation solvers. These two difficulties give rise to a third. Under extreme flow conditions, computational failures are quite common. Methods for “extending” the equations of state are often used to continue the computations. For example, below a certain arbitrary density, the JWL EOS is sometimes extended to the ideal-gas EOS. A fundamentally new method is presented in this work. It consists of using the much simpler Noble–Abel-stiffened-gas EOS as a predictor, to close the corresponding flow model. A thermodynamic relaxation step follows the prediction step. The solution is projected onto the target EOS, in this case the Mie–Grüneisen EOS, with the help of additional transport equations. Therefore, the flow model is an extended version, much more efficient for numerical resolution. This method solves the three problems above by extending the validity domain of the thermodynamic formulation, making the relaxation solvers much faster, and dramatically increasing the robustness of computations.

更新日期：2023-11-13

点击分享查看原文

点击收藏

公开下载

阅读更多本刊新发论文本刊介绍/投稿指南