An AdaptiveMesh FiniteDifference Solution Method for the NavierStokes Equations
Abstract
A variablespacing grid system for finitedifference calculations is presented. The system allows single points to be added to or deleted from the mesh independently of each other, while maintaining each point at the center of a symmetrical cross formed with four other mesh points. The single finitedifference form of the steady, incompressible NavierStokes equations necessary for use with this system is written in a suitable form insuring stability, and the additiondeletion procedure is easily automated and transformed into a selfadjusting algorithm capable of recognizing the highgradient regions of the solution field and selectively refining the mesh in those regions. It also determines the bestsuited number of points for the calculation. The method is finally applied to two test cases to show its performance.
 Publication:

Journal of Computational Physics
 Pub Date:
 February 1987
 DOI:
 10.1016/00219991(87)900593
 Bibcode:
 1987JCoPh..68..283L
 Keywords:

 Computational Fluid Dynamics;
 Computational Grids;
 Finite Difference Theory;
 NavierStokes Equation;
 Grashof Number;
 Isotherms;
 Iterative Solution;
 Nusselt Number;
 Fluid Mechanics and Heat Transfer