6.3.5. STEP 5 : Projection of vectors

It is implicitly admitted that the computaion lead to a solution in a galilean frame with a \((\vec{i}, \vec{j})\) basis. The velocity is in this frame, but the fluxes are computed in 1D way, in the normal direction of the face. It does mean that the fluxes are computed thanks to a Riemann solver in a local frame \((\vec{n_k}, \vec{ \tau_k})\). A change of frame is then necessary before the flux calculation \((\vec{i}, \vec{j})\) \(\longrightarrow\) \((\vec{n_k}, \vec{ \tau_k})\).

After that, it is necessary to do a new change of frame to put the fluxes back into the galilean frame in order to apply the finite volume relation Eq.1.6.