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.
[1]
S. F. Davis,et al.
Shock capturing with Padé methods
,
1998
.
[2]
Y. Adam,et al.
Highly accurate compact implicit methods and boundary conditions
,
1977
.
[3]
S. Osher,et al.
Weighted essentially non-oscillatory schemes
,
1994
.
[4]
Chi-Wang Shu,et al.
Efficient Implementation of Weighted ENO Schemes
,
1995
.
[5]
D. Gaitonde,et al.
Pade-Type Higher-Order Boundary Filters for the Navier-Stokes Equations
,
2000
.
[6]
Li Jiang,et al.
Weighted Compact Scheme for Shock Capturing
,
2001
.
[7]
S. Osher,et al.
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
,
1989
.
[8]
S. Lele.
Compact finite difference schemes with spectral-like resolution
,
1992
.