High-order BEM for potential transonic flows

• Published in: Computational mechanics 1998-04, Vol.21 (3), p.243-252
• Main Authors: IEMMA, U, MARCHESE, V, MORINO, L
• Format: Article
• Language: English
• Subjects: Boundary element method; Compressible flows; shock and detonation phenomena; Computational fluid dynamics; Computational methods in fluid dynamics; Euler-Lagrange equation; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Inviscid flows with vorticity; Laminar flows; Physics; Potential flows; Transonic flows; Two dimensional analysis; Two dimensional flow; Velocity distribution
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s004660050299

A high-order boundary element method (BEM) for the analysis of the steady two-dimensional full-potential transonic equation is presented. The use of a high-order (piecewise cubic on the boundary and piecewise bi-cubic in the field) numerical formulation, the main novelty of the present work, is important in two respects: first, the convergence of the solution as h vanishes is faster than the zeroth-order (the piecewise constant) one, yielding more accurate results with coarser grid resolutions. In addition, in supercritical flows, the derivation of the velocity field from the high-order representation for potential gives, in the vicinity of the shock, a sharper discontinuity, and allows for an in-depth analysis of the shock properties. Both aspects are analyzed in the present paper through applications to steady, two-dimensional, full-potential flows. All the results obtained using the present method are validated through comparison to other computational fluid dynamics (CFD) solutions of the full-potential flows and, when applicable, Euler equations. A comparison to a zeroth-order BEM, based on the same integral formulation is also included.