Full-potential integral solution for transonic flows with and without embedded Euler domains

Abstract

Two methods are presented to solve transonic airfoil flow problems. The first method is based on the integral equation solution of the full-potential equation in terms of the velocity field. A shock capturing-shock fitting scheme has been developed. In the shock-fitting part of the scheme, shock panels are introduced at the shock location. The shock panels are fitted by using the Rankine-Hugoniot relations. The second method is a coupling of the integral solution of the full-potential equation with the pseudotime integration of Euler equations, which are used in a small embedded region around the shock. This scheme is caUed the integral equation-embedded Euler scheme. The two methods are applied to NACA 0012 and 64A010A airfoils over a wide range of Mach numbers, and the results are in good agreement with the experimental data and other computational results. The schemes converge within a number of iterations that is one order of magnitude less than the finite-difference schemes.

High-order BEM for potential transonic flows

“…In contrast to Tseng and Morino (1982) (and all the subsequent papers cited above), where the ®eld sources include only the nonlinear terms, in Sinclair (1986Sinclair ( , 1988 the ®eld sources include all the compressibility terms (linear and nonlinear); this implies that the differential operator for the boundary integral formulation of Tseng and Morino (1982) is that of the wave equation, whereas for Sinclair (1986Sinclair ( , 1988 is the Laplacian and, as a consequence, a ®eld integral is required even for the linear case (subsonic¯ows). A shock-capturing shock-®tting (SCSF) scheme has been introduced by Kandil and Hu (1988), who use an integral formulation similar to that of Sinclair (1986Sinclair ( , 1988 for the shock capturing part of the algorithm, whereas a shock ®tting procedure is introduced by evaluating the shock strength and orientation using the Rankine-Ugoniot relations; the integral equation is modi®ed by introducing a source distribution on the shock surface, with intensity proportional to the local shock strength. The work of Kandil and Hu (1988) also includes the solution of the Euler equations by coupling the integral formulation with a ®nite difference solution of the Euler equation within a domain surrounding the shock.…”

“…A shock-capturing shock-®tting (SCSF) scheme has been introduced by Kandil and Hu (1988), who use an integral formulation similar to that of Sinclair (1986Sinclair ( , 1988 for the shock capturing part of the algorithm, whereas a shock ®tting procedure is introduced by evaluating the shock strength and orientation using the Rankine-Ugoniot relations; the integral equation is modi®ed by introducing a source distribution on the shock surface, with intensity proportional to the local shock strength. The work of Kandil and Hu (1988) also includes the solution of the Euler equations by coupling the integral formulation with a ®nite difference solution of the Euler equation within a domain surrounding the shock. Hu (1995) extends the shock-®tting ®eld panel method to three-dimensional steady transonic¯ows.…”