I meet some difficulty in defing interface spnic speed referred as Kyu Hong Kim suggessted. in details :

H-norm = 0.5*(HL-toal - 0.5*VL**2 + HR-toal - 0.5*VR**2) In this formula, how the define the tangential velocity V in curvilinear coordinate.because we can't know the oblique shock shape ans position. who can give me some detailed interpretation.thanks

Usually, we assume the shock wave is aligned with the grid interface according to Gudonov's theory. As a result, the tangential velocity= V- V.n, where V denotes the velocity vector and ndenotes the unit normal of cell interface. Of course, If the shock wave is not aligned with the grid interface, the captured shock wave will pass though several cells.