Monotone switches in implicit algorithms for potential equations applied to transonic flows

Abstract

Numerical calculations of transonic flows by potential equations typically use algorithms that change the method of calculation for regions of subsonic and supersonic flow. In this paper, implicit approximatefactorization algorithms are modified to use the monotonic switch in the type of finite differencing that was developed by Godunov for the Euler equations. Calculations of flows over airfoils by these algorithms are compared with calculations by other commonly used methods. For the small-disturbance potential equation, comparisons are made with the Murman-Cole method for both steady and unsteady flows. For the full potential equation, comparisons are made with the method of Hoist and Ballhaus for steady flows. The comparisons show that the monotone methods are more stable. For steady flows, converged solutions are obtained for cases where the older methods fail. For unsteady flows, solutions are obtained for cases where the Murman-Cole switch requires a time step more than ten times smaller in order for the calculations to remain stable. These improvements are achieved with no increase in computer storage and only minor modifications in current codes.