fatpigking 发表于 2023-6-1 13:21:54

简版NS方程用于CFD有完备性问题?这篇论文有看法

本帖最后由 fatpigking 于 2023-6-1 13:27 编辑

看了一篇论文,观点非常新颖,认为NS方程用于CFD有角动量损失的缺陷。全文逻辑严密,有理论分析且给出解决方案。通过仿真计算,揭示传统方法损失了角动量,而新方法克服了角动量损失问题。甚至理论推导了传统方法角动量损失的大小,并且与数值仿真结果高度匹配!由于其观点挑战常识,因此发帖请教各高手鉴定。
1.理论依据
众所周知,相对于角动量,NS方程是平动量方程。那么在NS方程控制的流场里,如何确保流动是符合角动量守恒的呢。论文表示,经典理论是利用本构方程实现的:本构方程的建立条件就是,假定了无限小物质的表面是力矩平衡的。通过在NS方程的粘性项中引入本构方程,从而确保角动量的守恒(平衡的力矩不改变角动量)。
但是论文很快又指出,多数时候用于CFD的简化版NS方程,其中的本构方程在简化过程中被消去了。因此,简版NS方程不含本构方程,模拟出的流场是不满足角动量守恒定律的!
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=========简化的NS方程
2.解决方案
为了克服这个问题,论文在二维情况下给出了新解决方案,通过增加一个角动量方程以确保角动量守恒。具体方法此处省略。
3.效果展示
论文做了简单的对比模拟计算。证明常规方法计算结果确实有力矩不平衡的问题(角动量不守恒),文中提供的新方法克服了这个问题,而且给出的流场分布有所不同。更让人惊奇的是,论文理论推导给出了NS方程流场残余力矩的大小(“等于粘性系数与流场涡环量的乘积”),与数值模拟结果符合很好!由于论文过于奇葩,特向各老师请教,如何评价这个论文。
论文名叫《有限体积法的粘性力矩问题及其改进》,获取链接在此https://pan.baidu.com/s/1yrucFbevfpb1QLjX2Hl0qw?pwd=qatp无法下载的留言邮箱,看见了会发过去。
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查看完整版本: 简版NS方程用于CFD有完备性问题?这篇论文有看法