A Fast-Solver Algorithm for Steady Transonic Potential-Flow Computations with Newton Iteration and Multigrid Relaxation

摘要

An algorithm based on an approximate Newton iteration of the nonlinear finite difference equations of transonic flow was tested on fully conservative potential flow around airfoils. It is found that the iteration to the circulation must be kept outside the multigrid algorithm. Meaningful residual norms, to be used in termination tests of loops, can be designed using finite-difference formulas with asymptotic scaling. Mass-flux-vector splitting solves instability problems encountered at sonic lines with artificial-viscosity terms. A special subalgorithm outside the multigrid algorithm is needed to update shock positions. The Newton/multigrid algorithm is very efficient for subsonic flows around airfoils with lift. For transonic flows, the algorithm is convergent.