Artificial compressibility methods for numerical solutions of transonic full potential equation

Entropy condition satisfying approximations for the full potential equation of transonic flow

“…The FP formulation is the most efficient of the three in terms of accuracy-to-cost ratio for a wide range of inviscid transonic flow applications for real geometries. TSD is valid for thin wings at free stream Mach numbers near unity, and EU, while the least restrictive, involves the most complicated system of equations.During the last few years, many numerical calculations using FP have been presented, e.g., [19], [14], [17], and [6]. The object of our present investigation is twofold.…”

“…During the last few years, many numerical calculations using FP have been presented, e.g., [19], [14], [17], and [6]. The object of our present investigation is twofold.…”

“…have been in use for some time, e.g., [6], [14], [17]. We now compare the x differencing in the algorithms of [6], [14], [17], with that of (4.4). Using E.O., we have (if 8X$ > 0 for all relevant points) Density Biasing.…”

“…In this section we shall give examples of schemes of the type (3.6), where the function h is an E flux. We shall compare these flux biasing algorithms, with the density biasing methods of [6], [14], and [17].…”

Application of two-point difference schemes to the conservative Euler equations for one-dimensional flows

“…If equations (5) and (6) are written in quasi linear form, these equations will have two characteristics with slopes given by (8) The directionality of the two characteristics is determined by the sign of equation (8) which is the same as the sign of u ± c where c is the local isentropic sound speed. The directionality of the characteristics at the boundary points will be used in a later section to determine how many boundary conditions may be applied at each boundary.…”