By H. W. M. Hoeijmakers (auth.), Prof. Dr.-Ing. Josel Ballmann, Prof. Dr. Richard Eppler, Prof. Dr. Wolfgang Hackbusch (eds.)
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Extra resources for Panel Methods in Fluid Mechanics with Emphasis on Aerodynamics: Proceedings of the Third GAMM-Seminar Kiel, January 16 to 18, 1987
The supers onic triplet - A new aerodynamic panel singui arity with di rectional properties", AIAA J ou r na l , Volo 18, No. 2 (1980), pp. 138-14 2 . , Rubbe r t , P. E. : "A co mpar ison of pa ne L me t hods fo r subs on ic f I ow c omput at i on", AGARDog raph No. 241 (19 79). : "Asymptotic convergence of h igher-order accurate panei methods", J. of Aircraft, Volo 23 , No. 2 (1986), pp. 126-130. , Hewitt, B. : "The ind irect boundary-integral formul ation for ellipt ic, hy pe rbo lic a nd non- linear fl ui d f I ows " , Ch .
1 6 )- [17 ]. This i s a pu z zling situation a nd one may wonder what causes th is ano maly , is th e analys is based on the sma ll-curv at ure expansion perhaps t oo c on se r vat ive, or is th e r e some hidden ann i h ilation of e r ro r te rrns i n th e proce s s of ob t ai ning ~ f rom Eq. ( 12) a nd the surface vel oc it y f r om Eq. (i 3 . b )? I: Neumann vs Dirichlet b oundary c ond i tion In this sect i on we consider some of the s t re n g t h s and weakne sses of me t ho ds th at empl oy th e Neumann boundary condit ion and methods that employ the Dirichlet boundary condition.
J= [TI b ,- V Iinversion of 1 b ]'[~J = r 1 Cl : ( Cl) - q results a fter the f irs t time step [~~J= / ( Cl)-l' r l ! m m + 1 matrix c o rnput a t ion at m -th time step: m] m m m V und T : Vm . [t = T . i [~~ I incorporat ion of boundary conditions: m (reorde ring ) - Cm und r res ults after t he m-rh rime step: [ur~J= no ( Cl )-1. " )·u m = I I unm -r'" n m =: u-r . (16) Fo r these equations, which correspond to (15), a program flow chart has been given in Fig. 2 which demonst rat es the sequence of the solution procedure steps, PRESSURE WAVES IN A SEMI-INFINITE FLUID OOMAIN In this section an application of the above procedures is presented which shows the correctness of the solution, and which also dernonst ra tes their advantages in the case of semi-infinite domains.
Panel Methods in Fluid Mechanics with Emphasis on Aerodynamics: Proceedings of the Third GAMM-Seminar Kiel, January 16 to 18, 1987 by H. W. M. Hoeijmakers (auth.), Prof. Dr.-Ing. Josel Ballmann, Prof. Dr. Richard Eppler, Prof. Dr. Wolfgang Hackbusch (eds.)