| Summary: | A novel semi-implicit scheme for the Navier-Stokes equations is presented and evaluated.
The semi-implicit scheme combines an implicit temporal integration in the bodynormal
directions with explicit temporal integrations in the streamwise and cross stream
directions. Thus, advantages of both explicit and implicit schemes are retained in the
semi-implicit scheme. Numerical stiffness due to disparate physical scales in the normal
direction is eliminated, since stability of the algorithm depends only on relatively coarse
streamwise and cross stream grid spacing, not on the typically fine normal spacing. Approximate
factorization is unnecessary and only one matrix inversion per multi-stage
time step is required. Computations show that while a explicit scheme employing multigrid
and residual smoothing and a fully implicit scheme are competitive for inviscid
calculations, the semi-implicit scheme is superior for viscous flow calculations.
Efficiency of the semi-implicit scheme is exploited in a study of flow separation
around delta wings with blunt leading edges. Three-dimensional laminar vortical flows
over two 65* swept semi-infinite elliptical wings of thickness to chord ratio 1 : 11.55 and
1 : 20 at Moo = 1.6, ReL = 106, and angles of attack of 40, and 8*, and a 60* swept
elliptical wing with t/c = 1 : 11.55 at Moo = 1.4, ReL = 2 x 106 and a = 14* are
considered. In these flow cases, separation line locations are fixed not by a particular
geometric factor (eg. sharp leading edge), but by interaction of physical and geometric
factors. Solutions with the semi-implicit scheme are shown to be significantly more
efficient than solutions with a corresponding explicit scheme. Two distinct leading edge
separation processes are identified: separation due to shock-less flow recompression leeward
of the leading edge expansion in the t/c = 11.55, a = 40 case and separation
involving a leading edge shock in the remaining cases.
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