A QuasiParabolic technique for computation of threedimensional viscous flows
Abstract
A computational technique is presented for obtaining flowfield solutions to a parabolic form of the NavierStokes equations. The point of departure is the General Interpolant Method (GIM) which provides a discretization for partial differential equations on arbitrary threedimensional geometries. The new scheme, termed QuasiParabolic, treats the parabolized equations but with 'timelike' terms appended. Addition of these extra terms, which are relaxed by iteration, avoid many of the singularities inherent in classical parabolic NavierStokes methods. Streamwise derivatives are approximated by threepoint backward differences and the cross plane operators use an alternating forwardbackward sweep. A twostep sequence is used to implement the difference scheme in the spatial dimensions and a timelike relaxation converges the quasiparabolic procedure at each plane. Solutions are presented for flows in two and three dimensions. Inviscid flows are solved for internal and external applications and viscous flows in boundary layers and free shear layers are also computed with the GIM/QuasiParabolic scheme.
 Publication:

AIAA, Aerospace Sciences Meeting
 Pub Date:
 January 1981
 Bibcode:
 1981aiaa.meetX....S
 Keywords:

 Computational Fluid Dynamics;
 Parabolic Differential Equations;
 Three Dimensional Flow;
 Viscous Flow;
 Algorithms;
 Finite Difference Theory;
 Flow Velocity;
 Microgravity Applications;
 NavierStokes Equation;
 Partial Differential Equations;
 Shear Flow;
 Space Commercialization;
 Fluid Mechanics and Heat Transfer