Numerical METHODS FOR Two-and Three-Dimensional Viscous Flow Problems: Applications to Hypersonic Leading Edge Equations,

摘要

Several explicit and implicit finite-difference methods,useful for treating two-and three-dimensional viscous flow problems,are compared. These techniques are applied to the single-layer equations previously developed by the authors for continuum leading-edge studies. Stability and accuracy of different schemes,effects of linearization,boundary conditions,coordinate systems and grid size,and the need for iteration are discussed. Solutions are presented for equilibrium and rotational non-equilibrium flow fields and comparisons with experimental data are provided. Different models for the pressure gradient (px) term in the streamwise momentum equation are discussed and it is shown that the effects of upstream influence appear in certain px representations that may be useful when these effects are important. The relationship to so-called sub-or super-critical flows is demonstrated. For three-dimensional geometries, a new predictor-corrector method is devised and tested for stability properties. For a right-angle corner geometry,solutions are compared with explicit results obtained with step sizes three orders of magnitude smaller. The need for iteration in obtaining accurate and consistent results is emphasized. The use of these techniques for two-dimensional unsteady Navier-Stokes solutions is discussed. (Author)