Boundary-fitted coordinate is mentioned in Many literatures.The processes are all that the Poisson equations in the physics plane are transformed to the ones in transformed plane.Here,I am confused by the reason why not the Poisson equations are given in the physics directly.That is to say,the transformation is not needed.The relation between the two planes on boundary is known.The uniformed grids in transformed plane are already made.The next thing is to solve Poisson equations and get the values of points in physics plane corresponding to the ones in transformed plane. Who can explain it to me?

Hi

If you don't transform the Poisson Equation and you are using finite difference, the x´s coordinates need to be equally separated in order to get a better approximation, but this is not the case. That is the reason why is needed change to transformed plane. Maybe I am not being so helpful, you should read COMPUTATIONAL FLUID DYNAMICS by John Anderson (Chapter 5), and sure you'll find all the information that you need.

Thanks for your explanation.But it appears that,to some extent, you have mistook my idea.

My idea is that we can give the Poisson equations in the phsics plane.That is to say,the Poisson equations' variables are eta and kese in transformed plane,and the variables that are needed to solve are x and y in physics plane.It just like that we solve the problem of pure,two-dimensional heat conduction in a domain of shape of rectangle.Here,transformed plane corresponds to the rectangle domain in the problem of pure heat conduction,and physics plane corresponds to the distribution of temperature.

That is my idea.Not only is there not the transformation,but also the variables and functions in the Poisson equations are put inversely.

Yes, you can. Indeed, both STAR-CD and Fluent solve all equations in the global Cartesian coordinates without transforming equations.

Solving d2A/de2 + d2A/dn2=0, where A=x,y.

The results are not what I expect. Actually, if I want to generate a mesh with irregular boundaries, the mesh doesn't describe the boundary correctly. And the only "correct" mesh generation seems to appear when the real plane is rectangular too.

dear yka how r u 1-refer to Hoffmann, K., and Chiang, S.(1995)"Computational Fluid Dynamics for Engineers", engineering Education System, Wichita, USA. chapter 9 2- the reason for using Boundary-fitted coordinate is the problem of boundary conditions for non rectangular body such as airfoil,so the governing equation is transformed from cartesiuan to curvilinear generalized coordinate system,and the grid must cluster at the body for petter performance,the construction of the grid points is down as follow Solution Steps: 1. Specify (x,y)of the points on the physical boundary. 2. Use linear interpolation to calculate (x,y) for interior points (Algebraic grid generation method). 3. Solve the equations (3.18) and (3.19) after discretisation to estimate the new values of x,y at interior points. 4. Update the values at the boundary (will be explained at the end of this section). 5. Calculate the difference between the new and old values of x,y 6. Return to step 3 if the solution does not converge (i.e. error >max.error)

if u need more details contact me at omrkhairy75@yahoo.com