Numerical Solution of the Full Potential Equation Using a Chimera Grid Approach

HE purpose of this Note is to present results from a new algorithm for solving the full potential equation based on a chimera grid approach. The long term objective of this work is to develop a chimera-based full potential flow solver that will be compatible with the well-established OVERFLOW Euler/Navier-Stokes flow solver.1"3 Thus, the user will have an option of which flow solver to use in the chimera-based zonal grid approach: full potential, Euler, or Navier-Stokes. Of course, the full potential option will not be applicable for all applications, but for those applications where the full potential equation is valid, the execution time should be up to two orders of magnitude less than for the Navier-Stokes formulation. Indeed, a chimera-based full potential solver should have modest execution times on even moderate-speed workstations. In a parametric study, the bulk of the required computations could utilize the full potential approach and then a few selected conditions could be checked with a more complete, and thus more accurate, Euler or Navier-Stokes simulation. Such an approach would be extremely cost effective especially considering that all of these approaches would utilize the same problem setup and postprocessing software and to a large extent the same grid generation software. For most chimera zonal grid applications, there is not much information on error analysis. The questions of how much error the interpolation process produces and what the effect is of this error on various aspects of the solution away from the interface boundary have not been generally addressed. One notable exception to this is the work of Meakin,4 in which a chimera scheme error analysis was performed for a number of steady and unsteady transonic airfoil cases. Results from this study demonstrated the viability of the chimera approach for the Euler formulation being used. The purpose of the present study is to investigate the prior two questions in the context of a chimera full potential solver.