Skew grids and irrotational flow
Abstract
Finitedifference computation of incompressible flow through regions of arbitrary shape often requires the implementation of boundaryfitted coordinates for which the grid lines may be nonorthogonal (skew). When the governing equations are expressed in terms of pressure and velocity, conservation of mass is maintained by the gradient of the pressure. In principle, the gradient is irrotational and should have no effect on the existing circulation in the flow field; but if the grid lines are skew, the discrete representation of the gradient can generate spurious vorticity near the boundaries. In the present work this difficulty is eliminated for uniform skew grids, and markedly reduced for nonuniform skew grids, by adopting a discrete formulation of the pressure gradient that helps maintain irrotationality near boundaries. The procedure is applicable for staggered grids with either Poisson or Chorin equations for pressure.
 Publication:

Fifth Army Conference on Applied Mathematics and Computing
 Pub Date:
 March 1988
 Bibcode:
 1988apmc.conf..631B
 Keywords:

 Computational Fluid Dynamics;
 Computational Grids;
 Finite Difference Theory;
 Incompressible Flow;
 Cartesian Coordinates;
 Flow Distribution;
 Pressure Gradients;
 Shapes;
 Velocity;
 Fluid Mechanics and Heat Transfer