用统一一阶双曲模型与保结构半隐式格式模拟非牛顿粘塑性流动
流体动力学
2021-04-27 v3 数值分析
数值分析
摘要
我们讨论了将连续流体与固体力学的统一双曲模型应用于非牛顿流动建模，特别是粘塑性流体（亦称屈服应力流体）流动中应力驱动的固液转变建模的适用性。与依赖纳维-斯托克斯理论非线性粘度概念并将固态表示为无限刚性不可变形固体的传统方法不同，我们的理论中固态是可变形的，而流体状态通过类似于麦克斯韦粘弹性理论的切向应力松弛过程被视为“熔化”的固体。该模型被表述为带可能刚性的非线性松弛源项的一阶双曲偏微分方程组。计算策略基于交错半隐式格式，其尤其可应用于低马赫数流动，正如非牛顿流体流动通常所需。模型与数值格式的适用性在几个标准基准测试用例上得到展示，如库埃特流、哈根-泊肃叶流与顶盖驱动空腔流。数值解与采用 Herschel-Bulkley 非线性粘度本构模型的纳维-斯托克斯理论的解析或数值解进行了比较。
引用
@article{arxiv.2012.07656,
title = {Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme},
author = {Ilya Peshkov and Michael Dumbser and Walter Boscheri and Evgeniy Romenski and Simone Chiocchetti and Matteo Ioriatti},
journal= {arXiv preprint arXiv:2012.07656},
year = {2021}
}
备注
The old title "Modeling solid-fluid transformations in non-Newtonian viscoplastic flows with a unified flow theory" has been changed to the title of the published version "Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme"