Hi,

I am doing fluid-structure interaction. There exists a code which solves the N.S eqns with FVM, and I am developing a code to deform the structure with FEM. At the interface I will transfer the stresses from the fluid to the solid mesh, and for that I need to interpolate from the FVM nodes to the FEM nodes. Initially, the domain is a cylinder.

I am thinking that the best way to achieve this is to find a function that goes through all the FVM nodes, and then use this function to calculate the value of the stress at the FEM nodes. For the moment I will consider the simplest form for the function, i.e. f(x,y,z)=Sum a(i,j,k) x^i y^j z^k, and this sum goes from 0 to 2 for i,j,k.

There are two thing that bother me: 1) The above function has 10 coefficients whose value will be determined by n points (n>10). I am thinking of the least square method for that. 2) Will this function be able to capture the abnormality of the surface?

Could someone suggest me a paper to read. I know that there is a lot of work on splines, and so I really need someone to direct me to the proper paper.

Thank you in advanced for your time

Do you use different elements for your NS and solids simulations? It would be easier to try a linear interpolation first before considering high-order interpolations assuming that your solutions do not use high-order schemes.

Yes, I do use different elements. On the face of a cell, the FEM has 9 nodes, but FVM has only 1 node. To improve the accuracy of the interpolation, for each FEM cell, there are 4 FVM cels. Thus, each FEM node is surrounded by 4 FVM nodes, except the nodes which are on the inlet/outlet boundary.

I could do a linear interpolation with these four FVM nodes, but this requires that I know which FVM nodes surround which FEM node. But, the only thing I have is a set of data.