3D interpolation: From FVM to FEM nodes and back
 

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

Re: 3D interpolation: From FVM to FEM nodes and ba
 

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.

Re: 3D interpolation: From FVM to FEM nodes and ba
 

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.