High-order compact finite-difference methods on general overset grids

• Published in: Journal of computational physics 2005-12, Vol.210 (2), p.459-496
• Main Authors: Sherer, Scott E., Scott, James N.
• Format: Article
• Language: English
• Subjects: Algorithms; Computation; Computational fluid dynamics; Computational techniques; Exact sciences and technology; Finite difference method; High-order methods; Interpolation; Laminar flow; Materials handling; Mathematical analysis; Mathematical methods in physics; Mathematical models; Overset-grid methods; Physics
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2005.04.017

This work investigates the coupling of a very high-order finite-difference algorithm for the solution of conservation laws on general curvilinear meshes with overset-grid techniques originally developed to address complex geometric configurations. The solver portion of the algorithm is based on Padé-type compact finite-differences of up to sixth-order, with up to 10th-order filters employed to remove spurious waves generated by grid non-uniformities, boundary conditions and flow non-linearities. The overset-grid approach is utilized as both a domain-decomposition paradigm for implementation of the algorithm on massively parallel machines and as a means for handling geometric complexity in the computational domain. Two key features have been implemented in the current work; the ability of the high-order algorithm to accommodate holes cut in grids by the overset-grid approach, and the use of high-order interpolation at non-coincident grid overlaps. Several high-order/high-accuracy interpolation methods were considered, and a high-order, explicit, non-optimized Lagrangian method was found to be the most accurate and robust for this application. Several two-dimensional benchmark problems were examined to validate the interpolation methods and the overall algorithm. These included grid-to-grid interpolation of analytic test functions, the inviscid convection of a vortex, laminar flow over single- and double-cylinder configurations, and the scattering of acoustic waves from one- and three-cylinder configurations. The employment of the overset-grid techniques, coupled with high-order interpolation at overset boundaries, was found to be an effective way of employing the high-order algorithm for more complex geometries than was previously possible.