## An algebraic homotopy method for generating quasi-three-dimensional grids for high-speed configurationsNational Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1989 - Mathematics - 73 pages |

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algebraic appears in Figure base shape blended wing-body configuration blended wing-body geometry blending functions body definition body geometries body surface coefficient computational space Computed pressure contours conformal mapping control functions coordinate cross-sectional shapes Curvilinear Coordinate defined denote diffeomorphism dimensional grid discrete point duct elliptic body end shapes exponent family of curves fighter aircraft Figure 21 finite-volume flow geometries flow solver given grid examples Grid line clustering Grid line concentration grid points homotopic procedure homotopy parameter inner and outer inner boundary intersecting trajectories NASA nearly orthogonal normalized orthogonal grids orthogonal trajectories outer boundary partial differential equations planar grids planform prescribed present method presented in Figure quasi-three-dimensional grid system scaling factor scaling function scheme sectional grid shape transition function shown in Figure smooth blending Smooth grid smooth map smoothly specified supersonic wing technique Three-view representation transfinite interpolation transformations transition function C(x transition surface values varies vector wing tips wing-body junctions x-station