Hello! I am treating the coupling between the fluid and the structure. To impose the interaction btw them, I have to impose following continuity relations

nf*uf=nf*us : continuity of normal displacements nf*vf=nf*vs : continuity of normal velocities nfp=ns*sigma : continuity of interface traction vector

where nf and ns are normal vecotr, and sigma is the stress tensor on the structure.

My questions on this subject are that

1. how to find normal displacments and velociteis. i.e., velocities consist of x-and y-directional component vx and vy, thus normal velocities are determined by vx*nx+vy*ny. How can I find the normal vectors to determine the normal values?

to do this first find local orthogonal curvilinear coordinate on desired point of interface (in 3d one basis is normal two of them are tangential), then you could decompose any (cartesian) vector into new coordinate, just with one matrix-vector product, than one component of this decomposition is your desired normal.