This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor fiowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid ...

The performances of absorbing boundary conditions (ABCs) in four widely used finite difference time domain (FDTD) methods, i.e. explicit, implicit, explicit staggered-time, and Chebyshev methods, for solving the time-dependent Schr dinger equation are assessed and compared. The computation efficiency for each approach is also evaluated. A typical evolution problem of a single Gaussian wave pack...

Numerical grid imprinting errors have often been observed in global atmospheric models on icosahedral grids. In this paper we analyse the sources of grid imprinting error related to the usual finite volume discretization of the divergence operator. We introduce the concept of alignment of computational cells, and establish that convergence of second order is attained on aligned cells. Moreover,...

A grid graph is a node-induced finite subgraph of the infinite grid. It is rectangular if its set of nodes is the product of two intervals. Given a rectangular grid graph and two of its nodes, we give necessary and sufficient conditions for the graph to have a Hamilton path between these two nodes. In contrast, the Hamilton path (and circuit) problem for general grid graphs is shown to be NP-co...

We prove that a pushing-block puzzle called PUSHPUSH-k is PSPACE-complete for any fixed k ≥ 1. In this puzzle, a robot moves on a finite grid. Each grid position is either empty or occupied by a single obstacle block. While moving, the robot may push obstacle blocks in direction of its movement, subject to certain constraints. In particular, once an obstacle block starts moving, it continues to...

A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to the treatment of boundary conditions imposed at radii larger than the size of the grid, following Abrahams, Rezzola, Rupright et al. [1]. In the method describ...

This paper extends the two-grid discretization scheme of the conforming finite elements proposed by Xu and Zhou (Math. Comput., 70 (2001), pp.17-25) to the nonconforming finite elements for eigenvalue problems. In particular, two two-grid discretization schemes based on Rayleigh quotient technique are proposed. By using these new schemes, the solution of an eigenvalue problem on a fine mesh is ...

A summary of the Lebedev finite-difference timedomain method, which is designed for modelling anisotropic problems in a simple and accurate manner, is provided. The basics of the method are presented, as well as augmentations to allow for coupling the Lebedev grid to standard Yee grid for more efficient use of memory; and implementation of conducting surfaces, and corners of 90◦ or 270◦.