Interface and Boundary Schemes for High-Order Methods


High-order finite-difference methods show promise for delivering efficiency improvements in some applications of computational fluid dynamics. Their accuracy and efficiency are dependent on the treatment of boundaries and interfaces. Interface schemes that do not involve halo nodes offer several advantages. In particular, they are an effective means of dealing with mesh nonsmoothness, which can arise from the geometry definition or mesh topology. In this paper, two such interface schemes are compared for a hyperbolic probem. Both schemes are stable and provide the required order of accuracy to preserve the desired global order. The first uses standard difference operators up to third-order global accuracy and special near-boundary operators to preserve stability for fifth-order global accuracy. The second scheme combines summation-by-parts operators with simultaneous approximation terms at interfaces and boundaries. The results demonstrate the effectiveness of both approaches in achieving their prescribed orders of accuracy and quantify the error associated with the introduction of interfaces. Overall, these schemes offer several advantages, and the error introduced at mesh interfaces is small. Hence they provide a highly competitive option for dealing with mesh interfaces and boundary conditions in high-order multiblock solvers, with the summation-by-parts approach with simultaneous approximation terms preferred for its more rigorous stability properties.

19th AIAA Computational Fluid Dynamics
X. Huan, J. E. Hicken, and D. W. Zingg. Interface and Boundary Schemes for High-Order Methods. In 19th AIAA Computational Fluid Dynamics, AIAA paper 2009–3658, San Antonio, TX, 2009.


address = {San Antonio, TX},
author = {Huan, Xun and Hicken, Jason E. and Zingg, David W.},
booktitle = {19th AIAA Computational Fluid Dynamics},
doi = {10.2514/6.2009-3658},
number = {2009-3658},
title = {{Interface and Boundary Schemes for High-Order Methods}},
year = {2009}