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 R.V.Ramkumar July 5, 1999 07:34

Elliptic Grid Generation

Hi, anybody

will you please tell me the literature for understand the basics of elliptic grid generation. i am unable to understand and which is the most efficient numerical technique for solving elliptic equations. thanks

 Robert Schneiders July 5, 1999 08:17

Re: Elliptic Grid Generation

Hi,

check Joe Thompson's classical text book:

http://WWW.ERC.MsState.Edu/misc/MSU_..._grid_gen.html

For more literature, take a look at

http://www-users.informatik.rwth-aac...iterature.html

Hope it helps

Robert

 John C. Chien July 5, 1999 11:06

Re: Elliptic Grid Generation

(1). Joe F. Thompson's Numerical Grid Generation book is online and is listed in this /resources/mesh generation/ section. (2). Joe Thompson and his math colleague developed the elliptic grid generation by solving a set of elliptic equations (something like a set of heat conduction equations with source terms.) back in 70's. (3). The 2-D grid generation was widely used in flow over an airfoil. NASA/Ames also has developed code using the elliptic grid generation in those days ( hope my memory is correct). (4). The method was extended to 3-D and a 3-D grid generation code was also developed in 80's. The code has been used by Air Force Labs. (5). It is easier to understand if you use the heat conduction problem as an example. For 2-D problem, you need to solve a set of two elliptic equations. One set of the solution will give you the y-mesh lines (something like the constant temperature contour lines in one direction), and the other set of the solution will give you the x-mesh lines (another set of solution to another heat conduction problem with the temperature gradient 90 degree to the first heat conduction problem). So, the y-mesh lines and the x-mesh lines are solutions to two equations ( or two problems). At this level, it should be straightforward to understand the concept behind, if you had taken the heat conduction course. (6). The difficulties of using the elliptic numerical grid generation is in the control of the mesh spacing locally in two directions. In heat conduction, the constant temperature lines ( isothermal lines) will change their relative positions when there is heat source in the domain. The elliptic mesh generation uses the similar concept and includes the source term functions in the elliptic equations. The control of the source terms and the boundary conditions becomes much involved. The exact control of the mesh is not easy to achieve, and require several iterations of trial-and -error. (7). Another difficulty is that for non-converged solution, it is possible that some mesh lines can be folded on top of each other. (8). So, the original concept of elliptic grid generation is easy to understand ( similar to a set of heat conduction problems), the exact control of the mesh requires experience. It may have opened a new field of mesh generation ( originally aimed at the complex geometry), but it also created a sets of uncertainty in the final mesh control.

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