Composite overlapping meshes for the solution of partial differential equations
Journal of Computational Physics
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Zonal embedded grids for numerical simulations of wall-bounded turbulent flows
Journal of Computational Physics
B-spline method and zonal grids for simulations of complex turbulent flows
Journal of Computational Physics
Journal of Computational Physics
A critical evaluation of the resolution properties of B-Spline and compact finite difference methods
Journal of Computational Physics
On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
Journal of Computational Physics
Compact finite difference method for American option pricing
Journal of Computational and Applied Mathematics
Generation of smooth grids with line control for scattering from multiple obstacles
Mathematics and Computers in Simulation
Journal of Computational Physics
A new time-space domain high-order finite-difference method for the acoustic wave equation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
A Fourth Order Hermitian Box-Scheme with Fast Solver for the Poisson Problem in a Square
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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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 Pade-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.