a simple differential operation question

phsieh2005 · December 16, 2009, 09:14

Dear CFD experts,

Can someone post websites that shows differential operations in cartesian/cylindrical coordinates?

What I am looking for specifcally is

grad(H^2), where H is a vector field. Thanks!

phsieh

DoHander · December 17, 2009, 11:52

Any classical Fluid Mechanics book should have the expression for gradient, divergence and rotor in cartesian, cylindrical and spherical coordinates.

Check for example the book of White - Fluid Mechanics

Do

phsieh2005 · December 20, 2009, 12:27

Hi,

Thanks for the reply! I do not have White handy. But, could not find what I am looking for in other Fluid Mechanics textbooks or internet.

Actually, what I am actually looking for is:

del (H^2), where H is a vector field and del is nabla. How do I write out the differential operation in Cartesian Coordinates?

Can someone help?

phsieh2005

DoHander · December 20, 2009, 22:44

Or ... you can try Google (it generally works):

http://en.wikipedia.org/wiki/Del_in_...al_coordinates

Here you have all your operators gradient, rotor and divergence in Cartesian, Cylindrical and Spherical coordinates.

DoHander · December 20, 2009, 22:53

Probably what you are looking for is:

$\nabla$ fg=f $\nabla$ g + g $\nabla$ f

where you will use f=v and g=v.

phsieh2005 · December 21, 2009, 07:36

Hi, DoHander,

Thanks!

phsieh2005

December 16, 2009, 09:14	a simple differential operation question	#1
phsieh2005 Senior Member Pei-Ying Hsieh Join Date: Mar 2009 Posts: 334 Rep Power: 18	Dear CFD experts, Can someone post websites that shows differential operations in cartesian/cylindrical coordinates? What I am looking for specifcally is grad(H^2), where H is a vector field. Thanks! phsieh

December 20, 2009, 12:27	del differential operator	#3
phsieh2005 Senior Member Pei-Ying Hsieh Join Date: Mar 2009 Posts: 334 Rep Power: 18	Hi, Thanks for the reply! I do not have White handy. But, could not find what I am looking for in other Fluid Mechanics textbooks or internet. Actually, what I am actually looking for is: del (H^2), where H is a vector field and del is nabla. How do I write out the differential operation in Cartesian Coordinates? Can someone help? phsieh2005

December 20, 2009, 22:53	Gradient rule	#5
DoHander Senior Member Join Date: Nov 2009 Posts: 411 Rep Power: 19	Probably what you are looking for is: $\nabla$ fg=f $\nabla$ g + g $\nabla$ f where you will use f=v and g=v.

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December 17, 2009, 11:52		#2
DoHander Senior Member Join Date: Nov 2009 Posts: 411 Rep Power: 19	Any classical Fluid Mechanics book should have the expression for gradient, divergence and rotor in cartesian, cylindrical and spherical coordinates. Check for example the book of White - Fluid Mechanics Do

December 20, 2009, 22:44		#4
DoHander Senior Member Join Date: Nov 2009 Posts: 411 Rep Power: 19	Or ... you can try Google (it generally works): http://en.wikipedia.org/wiki/Del_in_...al_coordinates Here you have all your operators gradient, rotor and divergence in Cartesian, Cylindrical and Spherical coordinates.

December 21, 2009, 07:36		#6
phsieh2005 Senior Member Pei-Ying Hsieh Join Date: Mar 2009 Posts: 334 Rep Power: 18	Hi, DoHander, Thanks! phsieh2005