Implicit approximate-factorization schemes for the efficient solution of steady transonic flow problems

Three-dimensional dual-potential procedure for inlets and indraft wind tunnels

“…9 A second over relaxation parameter co is used to scale the residual. Each of the Poisson equations for the vector potential functions is updated in a similar manner.…”

Viscous-inviscid interaction in transonic flow

“…In an attempt to improve the rate of convergence to the solution of inviscid transonic flows, Ballhaus, Jameson and Albert [1978] developed an implicit approximate factorization (AF) algorithm. The method was applied to the steady state transonic small disturbance equation…”

“…The first factorization introduced by Ballhaus, Jameson and Albert (1978] referred to as AFl corresponds to aN =-(a-x i+ 6 X )(a -6 y Pj+i 6 y) (3.25) where a is a positive number which is part of a parameter sequence chosen so as to optimize the rate of convergence of the algorithm (3.8).…”

Transonic flow potential method development at Ames research center

“…Since this work, many calculations using AF iteration schemes have been obtained including a number of other efforts from Ames: Goorjian [18], and Steger and Caradonna [19] for time-accurate full potential applications; Ballhaus et al [20] for steady two-dimensional TSD computations; Holst and Ballhaus [14], and Holst [15] for steady two-dimensional full potential computations; and Holst and Thomas [21] for three-dimensional full potential computations.…”

“…One widely used AF scheme, the so-called AF2 scheme, first presented by Ballhaus and Steger [17], and subsequently used to solve the steady TSD equation by Ballhaus et al [20] and the conservative full potential equation by Holst and Ballhaus [14], can be expressed by choosing the N-operator of Eq. (19) as follows:…”