Implicit finitedifference schemes with nonsimplyconnected grids  A novel approach
Abstract
The use of implicit schemes in the calculation of fully viscous internal flows has become more widespread in recent years. The use of implicit schemes, however, normally introduces restrictions upon the grids that can be used in computations. The present scheme removes many of these restrictions by introducing a mixed sheared and Otype grid structure which allows easy fitting of nearfield boundaries and farfield boundaries. This grid structure requires that a cellcentered rather than a nodecentered implicit scheme be developed. Increased flexibility in the choice of grids that can be used should not be limited by using a scheme whose coding structure is grid dependent. A novel approach to the structure of an approximately factored scheme is detailed in this paper, whereby the physical structure of the grid in use is transparent to the code. This is accomplished by using a technique commonly employed in finite element computations where the grid cells are arbitrarily numbered and celltocell connection tables are used to define the relationships between cells. This algorithm has been implemented on a multiple processor computer and appears to be easily moved to other architectures. The scheme is also structured such that the calculation of flux balances and application of the implicit, timelike marching operator are independent of the type of boundary conditions being used. This scheme can therefore readily be used for both internal and external flowfield calculations with minimal changes.
 Publication:

AIAA, Aerospace Sciences Meeting
 Pub Date:
 January 1984
 Bibcode:
 1984aiaa.meetR....N
 Keywords:

 Cascade Flow;
 Computational Fluid Dynamics;
 Computational Grids;
 Finite Difference Theory;
 Algorithms;
 Iteration;
 Leading Edges;
 NavierStokes Equation;
 Trailing Edges;
 Turbomachinery;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer