CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

steepest slope direction on the plane

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   July 7, 2005, 00:24
Default steepest slope direction on the plane
  #1
Patrick
Guest
 
Posts: n/a
The plane is given by three points(P1, P2, P3). It's 3D. How to get the the steepest slope direction vector on this plane? It looks like a high school geometry problem. But I forget those things. thanks!
  Reply With Quote

Old   July 7, 2005, 05:33
Default Re: steepest slope direction on the plane
  #2
Karthik
Guest
 
Posts: n/a
Hi Patrick ,

Create two vectors, Vector 1 = P2-P1 Vector 2 = P3-P1 The cross product of those two vectors will give you vector which represents the normal direction ( steepest gradient).

The above answer is for a single plane with its point representations. When an entire flow field is taken into consideration, the implementation differs depending upon the problem taken into consideration.

cheers karthik
  Reply With Quote

Old   July 7, 2005, 12:18
Default Re: steepest slope direction on the plane
  #3
Patrick
Guest
 
Posts: n/a
That's normal direction. What I mean is the steepest slope alone the plane. Thank you anyway.
  Reply With Quote

Old   July 7, 2005, 15:49
Default Re: steepest slope direction on the plane
  #4
Richard
Guest
 
Posts: n/a
If h is the height of the plane above a reference plane, the steepest slope is in the direction of grad(h).
  Reply With Quote

Old   July 7, 2005, 17:40
Default Re: steepest slope direction on the plane
  #5
Mani
Guest
 
Posts: n/a
Unless you specify some reference point, line, or plane, the expression 'steepest slope' has no meaning. Let's assume that your reference plane is the x-y plane at z=0, so you are interested in the steepest descent to zero altitude (z). The steepest descent from any point in space to this plane is simply described by a unit vector in z-direction (either positive or negative, depending on the position of that point). Now, all you need to do is to project that vector onto your plane. In general: Given a reference plane, find the normal vector on that reference plane, and project it onto your plane.
  Reply With Quote

Old   July 8, 2005, 02:36
Default Re: steepest slope direction on the plane
  #6
Karthik
Guest
 
Posts: n/a
Hi Patrick,

Find the gradient of the flow paramater ( eg velocity ) to determine its steepest slope. Consider the stencil arrangement of 9 cells in 2D and 27 in 3D around the partcular node of a cell in which the steepest slope has to be calculated.

cheers Karthik
  Reply With Quote

Old   July 8, 2005, 14:36
Default Re: steepest slope direction on the plane
  #7
Patrick
Guest
 
Posts: n/a
"Given a reference plane, find the normal vector on that reference plane, and project it onto your plane." But how to project? In which direction? That is the problem.

Now I derived the expression my self. Suppose the unit normal vector n(A,B,C). Here A,B,C is the vector component. (I use y not z as the elevation direction, sorry) Then the steepest slope in the plane is: (A*B/sqrt(A^2+C^2), -sqrt(A^2+C^2), C*B/sqrt(A^2+C^). (check the signs, not so sure)

For example: A plane parallel to the z axis, and has a angle of 45 degree with XZ plane. The unit normal vector(1/sqrt(2), 1/sqrt(2), 0), then the steepest slope direction (-1/sqrt(2), 1/sqrt(2),0).

Thank you all guys!
  Reply With Quote

Old   July 8, 2005, 16:05
Default Re: steepest slope direction on the plane
  #8
Mani
Guest
 
Posts: n/a
"But how to project? In which direction? That is the problem."

The projection of a vector onto a plane is uniquely defined. There is no ambiguity about "directions". And that's exactly what you're doing with your formula.
  Reply With Quote

Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

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


Similar Threads
Thread Thread Starter Forum Replies Last Post
[Gmsh] Problem with Gmsh nishant_hull OpenFOAM Meshing & Mesh Conversion 23 August 5, 2015 03:09
Normal vector, slope and aspect angle g_niro Main CFD Forum 0 February 2, 2011 18:24
Meshing a Mixing Plane using ICEM Will Anderson FLUENT 0 November 6, 2010 18:08
[Gmsh] boundaries with gmshToFoam‏ ouafa OpenFOAM Meshing & Mesh Conversion 7 May 21, 2010 13:43
thermal conductivity in plane &thickness direction sreenivas Siemens 1 February 21, 2008 06:27


All times are GMT -4. The time now is 08:40.