Computation of three‐dimensional transonic flows using two stream functions

Abstract

A computational method for three‐dimensional flows is presented in terms of two stream functions, which may be considered as two components of a generalized vector potential. An iterative scheme is developed such that only a sequence of two‐dimensional‐like problems, for each function, is solved. The convergence of the iterative scheme is studied based on von Neumann linear analysis. For transonic flow calculation, numerical methods used for potential flows are readily applied, namely artificial density and Zebra relaxation. Results of transonic flow calculations around a wing are presented.

Magnetohydrodynamics Using Path or Stream Functions

“…Hydrodynamic simulations based on stream functions or path functions have been slowly evolving over the past few decades. Stream function codes have been developed for steady flows in 3D (e.g., Pearson 1981;Chungyuan & Dulikravich 1986;Sherif & Hafez 1988;Beale 1993;Knight & Mallinson 1996;Elshabka & Chung 1999). Path function simulations have been so far presented for time-dependent flows in 1D (Hui 2007) and in 2D (Loh & Hui 2000).…”

Numerical simulations of transonic aerodynamic flows based on a hierarchical formulation

“…Alternative formulations to the standard Euler and Navier-Stokes equations can be based on generalized Cauchy=Riemann equations [9][10][11][12], stream functions [33,34], or potential functions with corrections to account for rotational ow ÿelds. In this paper, numerical results are presented based on a hierarchical approach, with the potential ow solver as a base for both inviscid and viscous ows.…”

A three-dimensional dual potential procedure for rotational flows

“…Other alternate formulations using the Clebsch velocity decomposition have been presented by Grossman (1983) to compute inviscid supersonic conical flows, and by Chang and Adamczyk (1983) to compute inviscid subsonic rota tional flow in turning channels. Sherif and Hafez (1983) presented a scheme for solving irrotational transonic flow using two stream functions and discussed possible extensions to rotational flow. Morino (1985) derived a set of equations for unsteady, compressible viscous flow.…”