[kov]

Hello Everyone,

I am trying to write my own c-mesh elliptic grid generator over an airfoil in matlab using the conventional equations of

A d^2 x / d xi^2 - 2 B d^2 x / d xi d eta + C d^2 x / d eta^2 = 0

A d^2 y / d xi^2 - 2 B d^2 y / d xi d eta + C d^2 y / d eta^2 = 0

with

A = (d x / d xi)^2 + (d y / d xi)^2

B = (d x / d xi)(d x / d eta) + (d y / d xi)(d y / d eta)

C = (d x / d eta)^2 + (d y / d eta)^2

I have not done this before, and don't have experience in mesh generation. I have looked online (google is my friend) for the basic concepts and procedures on how to create this mesh. I have started my own code which runs, however I result in "circumferential" grid lines around the airfoil extending to the far-field boundaries, however I do not get any "radial" lines which would make it an actual mesh.

so far I have:
discretized the equations using 2nd order finite difference for all derivatives
created the airfoil and the boundaries for the c-mesh
initialized the solution using transfinite interpolation
solved the equations using a 2 v-cycle mutli-grid method

My goal in this thread is to try to find out where I am going wrong in my code, or identifying what concept I am not fully understanding with grid generation, or identify what I am missing in my code.

I would really appreciate your help with this thank you.