| 查看: 989 | 回复: 1 | |||
[交流]
numerical stiffness 怎么理解？ 已有1人参与
|
| The Navier-Stokes equations as expressed in Equation XXX become (numerically) very stiff at low Mach number due to the disparity between the fluid velocity and the acoustic speed (speed of sound). This is also true for incompressible flows, regardless of the fluid velocity, because acoustic waves travel infinitely fast in an incompressible fluid (speed of sound is infinite). The numerical stiffness of the equations under these conditions results in poor convergence rates |
回复此楼» 猜你喜欢
最失望的一年
已经有8人回复
-
存款400万可以在学校里躺平吗
已经有27人回复
-
请教限项目规定
已经有4人回复
-
拟解决的关键科学问题还要不要写
已经有8人回复
-
推荐一本书
已经有16人回复
-
国自然申请面上模板最新2026版出了吗？
已经有20人回复
-
26申博
已经有3人回复
-
基金委咋了？2026年的指南还没有出来？
已经有10人回复
-
基金申报
已经有6人回复
-
疑惑？
已经有5人回复
» 本主题相关价值贴推荐，对您同样有帮助:
★ ★ ★
小木虫: 金币+0.5, 给个红包，谢谢回帖
xiegangmai: 金币+2, 谢谢参与 2012-12-09 10:42:38
小木虫: 金币+0.5, 给个红包，谢谢回帖
xiegangmai: 金币+2, 谢谢参与 2012-12-09 10:42:38
|
In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small. It has proved difficult to formulate a precise definition of stiffness, but the main idea is that the equation includes some terms that can lead to rapid variation in the solution. When integrating a differential equation numerically, one would expect the requisite step size to be relatively small in a region where the solution curve displays much variation and to be relatively large where the solution curve straightens out to approach a line with slope nearly zero. For some problems this is not the case. Sometimes the step size is forced down to an unacceptably small level in a region where the solution curve is very smooth. The phenomenon being exhibited here is known as stiffness. In some cases we may have two different problems with the same solution, yet problem one is not stiff and problem two is stiff. Clearly the phenomenon cannot be a property of the exact solution, since this is the same for both problems, and must be a property of the differential system itself. It is thus appropriate to speak of stiff systems. |
2楼2012-12-09 10:38:04