Algebraic Grid Generation about a Fin-Afterbody Configuration.

The problem treated in this report is the generation of a surface fitted grid in the stern region of an undersea vehicle, specifically an axisymmetric pointed afterbody with four identical, symmetric, constant chord fins. In many respects this problem is similiar to the wing-fuselage problem. The desired grid is to be used for either inviscid or viscid incompressible flow calculations and hence must have proper clustering ability to resolve regions of high flow gradients. An algebraic approach is used which is an outgrowth of earlier 3-D grid generation work on a fin-cylinder configuration. An algebraic procedure is presented for the generation of a smooth computational grid about an afterbody-fin configuration. The method makes use of a sequence of conformal transformations to unwrap the geometry and remove the corner singularities at the fin trailing edge and tail of the afterbody. A 3-D grid is generated by stacking a sequence of 2-d grids of the C-type on predetermined, smooth tubular surfaces. Clustering is accomplished by a sequence of one-dimensional stretching functions in physical space. Examples are presented to show the character of the resulting grid. The computer code, which also contains a users manual, is available from the author.