Uni-directional implicit acceleration techniques for compressible Navier-Stokes solvers

摘要

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 pseudotime. ^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 matrix 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. ^(Author)