Interpolated Boundary Conditions
I am trying to develop a new boundary condition for a university code written in Fortran. The code is a finite volume solver. This interpolated boundary condition takes a previous solution, 1-D or 2-D, and uses that solution as an inlet for another solution. The reason I am doing this is to be able to split a problem into many parts where the outlet for one solution would be the inlet of another. The problem is I don't know how to begin to tackle this problem. I'm not sure of what type of interpolation to do or how to prescribe the solution of one grid onto an entirely different grid. I am seeking help in this area. Does anyone have any papers or any other sources I could look at to help with this problem?
To narrow down the problem I am specifically looking to take a 2-D Tecplot slice from one solution to use as an inlet for another computation. Any help is appreciated.
some personal opinions
the essence of your question is an interpolation method;
generally, for two entirely differnt grids, it is not easy to find a good interpolation method;
however, some simple methods could provide premilary solutions;
for example, if you want to define a value of a point (P) in your new grid system,
then you draw a circle with P point as the center, r as radius;
only taking into all the points (in the old grid system) locate in this circle, do a arithmetic mean;
for me, i will add some weighting factor, according to the distance and the problems;
you can search some paper about DEM method, as interpolation method is a key issue for this method;
best wishes !
Well i figured out how to do it. I used a distance weighted average to get the values for the new grid. I could have used a more elegant method to get the 4 nearest points but I don't have time for elegance.
I think for 1D it is fairly easy, it will be more difficult for multi-dimensional problem in particular if you have unstructured meshes. In that case I would suggest you to use the Radial Basis Functions, RBF. It is not that difficult, it is actually very easy to implement. Just my thoughts.
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