High-order compact scheme for boundary points

Abstract

In this paper, we introduce a new high-order scheme for boundary points when calculating the derivative of smooth functions by compact scheme. The primitive function reconstruction method of ENO schemes is applied to obtain the conservative form of the compact scheme. Equations for approximating the derivatives around the boundary points 1 and N are determined. For the Neumann (and mixed) boundary conditions, high-order equations are derived to determine the values of the function at the boundary points, 1 and N, before the primitive function reconstruction method is applied. We construct a subroutine that can be used with Dirichlet, Neumann, or mixed boundary conditions. Numerical tests are presented to demonstrate the capabilities of this new scheme, and a comparison to the lower-order boundary scheme shows its advantages.

Keywords:

• compact scheme
• high order
• boundary points
• conservative
• reconstruction

2000 AMS Subject Classification :

• 37M05

Acknowledgements

This work was supported by US AFOSR Grant FA9550-05-1-0136 supervised by Dr Fariba Fahroo and Air Force VA Summer Faculty Research Program supervised by Dr Datta.Gaitonde.