The Spatially Nonuniform Convergence of the Numerical Solutions of Flows
Abstract
The spatial distribution of the numerical disturbances that are generated during a numerical solution of a flow is examined. It is shown that the distribution of the disturbances is not uniform. In regions where the structure of a flow is simple, the magnitude of the generated disturbances is small and their decay is fast. However in complexflow regions, as in separation and vortical areas, largemagnitude disturbances appear and their decay may be very slow. The observed nonuniformity of the numerical disturbances makes possible the reduction of the calculation time by application of, what may be called, the partialgrid calculation technique, in which a major part of the calculation procedure is applied in selective subregions, where the velocity disturbances are large, and not within the whole grid. This technique is expected to prove beneficial in largescale calculations such as the flow about complete aircraft configurations at high angle of attack. Also, it has been shown that if the NavierStokes equations are written in a generalized coordinate system, then in regions in which the grid is fine, such as near solid boundaries, the norms become infinitesimally small, because in these regions the Jacobian has very large values. Thus, the norms, unless they are unscaled by the Jacobian, reflect only the changes that happen at the outer boundaries of the computation domain, where the value of the Jacobian approaches unity and not in the whole flow field. Inc.
 Publication:

Journal of Computational Physics
 Pub Date:
 June 1989
 DOI:
 10.1016/00219991(89)900570
 Bibcode:
 1989JCoPh..82..429P
 Keywords:

 Computational Fluid Dynamics;
 Convergence;
 Flow Distribution;
 Nonuniform Flow;
 Numerical Analysis;
 Aircraft Configurations;
 Angle Of Attack;
 Flight Envelopes;
 Jacobi Matrix Method;
 NavierStokes Equation;
 Separated Flow;
 Spatial Distribution;
 Vortices;
 Fluid Mechanics and Heat Transfer