# elliptic grid generation (orthogonal)

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 November 24, 1998, 21:33 elliptic grid generation (orthogonal) #1 vasu Guest   Posts: n/a i am trying to generate an orthogonal grid based on elliptic equations. i was reading several papers such as that by steger and sorenson, jcp,v33,1979. the problem is that of a circle in a rectangular domain. the grid lines should be normal on the circle (1st boundary) and on the rectangular boundary (second). the rectangle is quite large compared to circle. (imagine a circle of radius 1 unit at the center of a rectangle of size 4x20). (it will be much better if the grid is orthogonal throughout the domain though) i keep having problems with the method of control functions. for instance, which control functions are suitable? also, how do we calculate d2X/deta2 on the outer boundary?(eta is the vertical coordinate in computational domain and X is the horizontal coordinate in physical space) steger and sorenson give an expression for inner boundary as: d2x/deta2 (xi,0)=(-3.5*X(xi,1)+4.*X(xi,2)-.5*X(xi,3))/deta**2-3*dxdeta@(xi,1)/deta i am not sure how this is obtained and also, how this expression will look for d2x/deta2(xi,etamax=jm) any suggestions? thanks in advance.

 November 25, 1998, 06:32 Re: elliptic grid generation (orthogonal) #2 andy Guest   Posts: n/a The topology of your solution region precludes an orthogonal grid. Where do you want the non-orthogonalities? How many blocks can you use? The combination of "orthogonality" and "control functions" is unusual but I am not familiar with the work sited. Do you require orthogonality or is it simply desirable? If required, does it need to be conformal? If orthogonality is required, I would be suspicious of any source terms (if that is what your "control functions" are) and stick to the basic equations and manipulate through the boundary conditions. However, if it is only desirable and you really want to use "control functions" then tap into some of the stuff from J.F.Thompson.

 November 25, 1998, 12:47 Re: elliptic grid generation (orthogonal) #3 Vasu Veerapaneni Guest   Posts: n/a i was having problems even without orthogonality, when the rectangular outer boundary is bigger than the circle (i.e, the small side of rectangle is comparable, but the long side is, say, 10 times larger than circle). in such a case when i solve the elliptic equations: alpha*d2X/dxi2-2*beta*d2Xdxdeta+gamma*d2Xdeta2=0, similar for Y i get most of the grid lines in almost a square around the circle. i generate initial grid by drawing rays out of the center of circle and see where they intersect the circle and outer rectangle (gives grid points on the circle as well as rectangle) and interpolate inbetween for intermediate points. solution is slightly better if i calculate the derivatives for the coefficients using cubic spline method rather than the finite difference methods! Orthogonal: eventually i want to calculate drag force on the circle when a fluid is going through the rectangle. isn't it better to have the grid lines orthogonal to the circle. regarding outer boundary, the top will be free surface, and the bottom will be a solid surface. so, i would prefer orthogonality at these two surfaces also! any suggestions are greatly welcome. i am new to this area! thanks a lot!!! p.s.: i am not familiar with the blocks method. so, i am trying to generate a single grid for the whole domain.

 November 30, 1998, 23:45 Re: elliptic grid generation (orthogonal) #4 Tom Wanat Guest   Posts: n/a I can't answer your questions about the control functions from Steger and Sorenson, but I suggest you investigate the method for controlling orthogonality by using Poisson equations for xi and eta. An excellent description is found in "Numerical Methods for Engineers and Scientists" by Joe Hoffman. I used this method and found it relatively easy to understand and implement. Good luck.

 March 18, 2011, 06:13 #5 New Member   siddhaling Join Date: Mar 2011 Posts: 6 Rep Power: 14 hey buddy i am just new to CFD and i have a C code for one cylinder placed in rectangular domain; i need to apply orthogonality on the surface of the cylinder and in the inner surface of the rectangle . if u have an algorithm/code for it then please mail it to me ; email id: siddhaling@gmail.com thanks in advance

 March 19, 2011, 15:51 #6 Senior Member   John Chawner Join Date: Mar 2009 Location: Fort Worth, Texas, USA Posts: 275 Rep Power: 17 When it comes to structured grids, smoothing them with an elliptic PDE-based method, and enforcing angle and spacing constraints on the boundaries the method you cite (Steger and Sorenson) is an excellent method and probably the grandfather of them all. A similar method is by von Lavante, Hilgenstock, and White. The two methods differ in that the form (SS) enforces the angle and spacing constraints on the boundaries in an approximate manner while vLHW enforces them fairly precisely. For any questions about elliptic grid generation methods, the primary reference should be Thompson's Numerical Grid Generation: http://www.hpc.msstate.edu/publicati...book/index.php For SS (as embodied in the GRAPE code), here's a new-ish reference: http://www.hpc.msstate.edu/publicati...book/index.php It's harder to find an online reference for vLHW. You are taking the right approach to the problem and hopefully the references I've provided will help. For the record, these methods are implemented in our software for years and are at the core of our structured grid capabilities. __________________ John Chawner / jrc@pointwise.com / www.pointwise.com Blog: http://blog.pointwise.com/ on Twitter: @jchawner

 March 24, 2011, 06:22 grid orthogonality #7 New Member   alfurqan Join Date: Mar 2011 Posts: 1 Rep Power: 0 Hi, I m also generating the grid over cylinder but i want the notes of steger and sorenson. if u have this notes then plz send it at my email id- alfurqan@in.com Thanking u

 October 1, 2015, 14:30 #8 New Member   Gorkem Ocalan Join Date: Feb 2015 Posts: 5 Rep Power: 10 Hi everyone, I am looking for Steger, J.L., Sorenson, R.L.: Automatic mesh-point clustering near a boundary in grid generation with elliptic partial differential equations. J. Comp. Physics, vol. 39, 1979. if anyone sends it to me, I will appreciate gorkem.ocalan@gmail.com Thanks for your concern, Last edited by gorkemocalan; October 29, 2015 at 01:53.

October 28, 2015, 15:20
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Quote:
 Originally Posted by vasu ;1177 i am trying to generate an orthogonal grid based on elliptic equations. i was reading several papers such as that by steger and sorenson, jcp,v33,1979. the problem is that of a circle in a rectangular domain. the grid lines should be normal on the circle (1st boundary) and on the rectangular boundary (second). the rectangle is quite large compared to circle. (imagine a circle of radius 1 unit at the center of a rectangle of size 4x20). (it will be much better if the grid is orthogonal throughout the domain though) i keep having problems with the method of control functions. for instance, which control functions are suitable? also, how do we calculate d2X/deta2 on the outer boundary?(eta is the vertical coordinate in computational domain and X is the horizontal coordinate in physical space) steger and sorenson give an expression for inner boundary as: d2x/deta2 (xi,0)=(-3.5*X(xi,1)+4.*X(xi,2)-.5*X(xi,3))/deta**2-3*dxdeta@(xi,1)/deta i am not sure how this is obtained and also, how this expression will look for d2x/deta2(xi,etamax=jm) any suggestions? thanks in advance.
Hello I am generating an elliptic grid but I am facing some problem. Could you please send me the code for elliptic grid over airfoil.