The viscous terms are treated using a Galerkin Finite Element method on linear triangular elements. This approach does not guarantee the positivity of k and epsilon. Therefore, the convective fluxes for the turbulent equations are computed using the PSI fluctuation splitting scheme which is positive and linear preserving. The boundary and initial conditions are classical. In particular, a Stegger-Warming flux splitting scheme is used for inflow and outflow boundaries.
Time integration is explicit.
For unsteady computations, it is important to have a precise time integration scheme. In the first case, the use of mesh adaption technique was necessary in order to achieve a computational mesh with needed characterstics. We can see that the shock position is well computed. Transonic airfoil flow, computational mesh. Transonic airfoil flow, iso-lines of Mach number Ma .