Application of multigrid and adaptive grid embedding to the two-dimensional flux-split Euler equations

A numerical algorithm is presented for solving the two-dimensional flux-split Euler equations using a multigrid method with adaptive grid embedding. The method uses an unstructured data set along with a system of pointers for communication on the irregularly shaped grid topologies. An explicit two-stage time-advancement scheme is implemented. A multigrid algorithm is used to provide grid level communication and to accelerate the convergence of the solution to steady state. Results are presented for a NACA 0012 aerofoil in a free stream with a Mach number of 0.85 and an angle of attack of 1.0 degree. Excellent resolution of the shock structures is obtained with the adaptive grid embedding method with significantly fewer grid points than the comparable structured grid.