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Supersonic conical flow computations using a rectangular finite volume methodWhitaker, David Lee January 1986 (has links)
A method is developed to solve the conical flow equations in spherical coordinates using a rectangular finite volume approach. The only mapping done is the mapping of the spherical solution surface to that of a flat plane using a stereographic projection. The mapped plane is then discretised into rectangular finite volumes. The rectangular volumes are allowed to intersect the body surface in an arbitrary manner. A full potential formulation is used to represent the flow-field velocities. The full potential formulation prevents the formation of vortices in the flow-field but all other essential features of the supersonic conical flow are resolved. An upwind density shift is used to introduce an artificial viscosity in a conservative manner to eliminate non-physical expansion shocks and add numerical damping. The rectangular finite volume method is then extended to deal with infinitely thin conical fins. Numerical tests of cones, elliptical cones, conical wing-bodies and waveriders (with very thin winglets) have been done. Very good agreement with experimental results is found. / M.S.
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