Home > Forums > Software User Forums > OpenFOAM > OpenFOAM Programming & Development

Mathematic expression of grad(U)

Updated Threads

Search this Thread

Prev

Previous Post

Next Post

Next

November 24, 2015, 07:35	Mathematic expression of grad(U)	#1
Tobi Super Moderator Tobias Holzmann Join Date: Oct 2010 Location: Tussenhausen Posts: 2,708 Blog Entries: 6 Rep Power: 51	Hi all, I have just one question. In mostly all literature we find the gradient of a scalar $\vec \nabla \phi$ or vector $\vec \nabla \textbf{U}$ in that way. But in a mathematic point of view this is not correct for vectors. So we get for any scalar: $\mathrm{grad}(\phi) = \vec \nabla \phi = \sum_{i=1}^{3} \frac{\partial \phi}{\partial x_i} \vec e_i$ Of course I assume $\vec \nabla$ as the partial differentials of the three directions and this is correct but For any vector: $\mathrm{grad}(\textbf{U}) = (\vec \nabla \otimes \textbf{U})^T = (\vec \nabla \textbf{U})^T$ My question now. Is it just a definition that we suppose that everybody know that $\vec \nabla \textbf{U}$ is the transposed dyadic product of these two vectors? Because normally, $\vec \nabla$ and $\textbf{U}$ are two vectors with the matrix notation (3x1) and (3x1). Therefore we have to use the dyadic product of this operation and after that we really have to transpose that matrix to get the correct form of the gradient matrix. Example: $\vec \nabla \textbf{U} = \vec\nabla \otimes \textbf{U} \neq \mathrm{grad}(\textbf{U})$ $(\vec \nabla \textbf{U})^T = (\vec\nabla \otimes \textbf{U})^T = \vec\nabla \textbf{U}^T \overset{!}{=} \mathrm{grad}(\textbf{U})$ Again. Is it a definition that in CFD numerics we say: $\vec \nabla \textbf{U} \overset{!}{=} (\vec \nabla \textbf{U})^T$ I would kindly appreciate some feedback. __________________ Keep foaming, Tobias Holzmann Last edited by Tobi; November 24, 2015 at 11:36.

« Previous Thread | Next Thread »

Posting Rules
You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Trackbacks are Off Pingbacks are On Refbacks are On Forum Rules

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Outlet boundary condition in interFoam	Andrea_85	OpenFOAM Running, Solving & CFD	51	July 20, 2017 13:31
writing execFlowFunctionObjects	immortality	OpenFOAM Post-Processing	30	September 15, 2013 06:16
How to install CGNS under windows xp?	lzgwhy	Main CFD Forum	1	January 11, 2011 18:44
CGNS lib and Fortran compiler	manaliac	Main CFD Forum	2	November 29, 2010 06:25
Lift, Drag Vs time chart,calculations	Jamesd69climber	CFX	8	February 17, 2005 17:23

All times are GMT -4. The time now is 06:17.