When transforming equation into curvilinear system is the boundary condition applied in physical/ computational space?

Shuo

The answer depends on the kind of transformation that you employ. When you transform the velocity components you can use covariant or contravariant transformation or you can just assume each component as a scalar and perform the transformation in the usual way.

Lets consider the case of Euler eq. The BC you set is U.n=0. If the grid is curvilinear and you perform coordinate transformation from cartesian (u,v) to curvilinear (assume u1,u2). In the transformed space because of no penetration condition

u2=0 and u2 is related to cartesian by u2= u dphi/dx+ v dpi/dy and using u2=0 you get the BC.

Check the 4th Aeroacoustic workshop on benchmark problems (available from NASA server ) and look for papers by Visbal and Scott.

Harish