I have a problem to solve a flow in isosceles inverted triangular duct how can i take points inside the triangle through for loop using finite difference scheme

I have a problem to solve a flow in isosceles inverted triangular duct how can i take points inside the triangle through for loop using finite difference scheme

Answer 1

[John D'Errico]

Not even remotely a MATLAB question, since you have no idea how to solve the problem.

I assume you have a PDE over the domain, and want to use finite differences to build a solution. The problem is a classical finite differnce does not seem well suited to the non-rectangular domain. I would suggest some alternatives.

Formulate the problem in terms of a triangulation of the domain. This is very well suited, since your domain already is triangular. So you would simply refine that triangle into a triangular mesh. Having done that, if you absolutely want to stick with a finite difference solution, I suppose you could formulate finite differenece approximations for the necessary deriviatives at each node of the triangulation. This would not be at all difficult, and the triangulation would be a nice regular one. For example, consider this paper, where they describe the use of FDA on a hex-mesh.:

http://www.ness.music.ed.ac.uk/wp-content/uploads/2013/02/hamilton2013hexagonal-1.pdf

Next, you might consider other schemes, perhaps Galerkin type methods. Again, a trimesh seems like it would be appropriate here.

[zia khan]

thanx for your valuable comments.can you plz elaborate how to use the FD scheme for triangualtion

[John D'Errico]

And this is why I initially stated this is not a question for Answers. Your question is still many steps away before it becomes something remotely about MATLAB. I gave you a link that discussed the problem. In fact, a simple search on "finite difference methods on a triangulated mesh", or something like that, will give you many hits.

I won't read the paper (or find one that is more pertinent to your specific problem), extract the necessary formulas, then form a triangulation of some domain for you, and show how to implement this all in MATLAB to solve some vague, barely specified problem. Is there even areason why the PDE tools in MATLAB do not apply to your problem? (Probably because your problem is not an elliptic one?) So, does the PDE toolbox apply to your problem? (Actually, probably not, but it has been too many years since I did these things in any seriousness to know positively.)

https://www.mathworks.com/help/pde/index.html

The point is, in order to solve such a problem, you need to understand the methods appropriate for your class of problem. We have not even been told that. So I would suggest that you consult directly with someone with skills in this area of mathematics, or you need to do a lot of reading.