An alternating direction implicit finite element method for compressible, viscous flow

The paper describes the application of a Galerkin finite element formulation to the equations governing unsteady compressible viscous flows, followed by an alternating direction implicit treatment of the algebraic equation at every time step. This formulation replaces the global factorization at every time step with the repeated solution of a tridiagonal system of equations associated with every grid line; this is both economical in execution time and in memory requirements. The method is fourth-order accurate in space and, for the thermal entry problem the best scheme is unconditionally stable. For viscous compressible flow this scheme is subject to a time-step restriction for Reynolds numbers of practical interest.