Uni-directional implicit acceleration techniques for compressible navier-stokes solvers

We solve the steady-state compressible Navier-Stokes equations around complex aerodynamic bodies. A central difference scheme is used augmented by a matrix valued artificial viscosity. To reach a steady state a multi-stage algorithm is used to march the solution in pseudo-time. Multigrid is then applied to further accelerate the convergence to a steady-state. However, because of the high aspect ratio, cells that are needed to resolve the turbulent boundary layers at high Reynolds numbers this scheme still requires thousands of sweeps through the mesh. To further accelerate the convergence a block implicit method is added to the above algorithm. Because of difficulties with A.D.I. methods this implicit operator is added in only one direction, usually normal to the boundary layer. To partially account for the other directions the complete linearized Jacobian is included in the diagonal term of the implicit operator. Hence, a block tridiagonal ma trix needs to be inverted at each stage of the multistage scheme. This method can also be adapted to include a low speed preconditioning to accelerate the convergence rates at small Mach numbers. Results are presented for flow about an ONERA wing at several different inflow Mach numbers.