Parameterization in Grid Generation

The distribution of grid points for calculating the solution of partial differential equations is chosen so as to include consideration of truncation error, stability, and the resolution of the solution near boundary layers and shocks. It is important to specify the distribution of points along a grid line. The problem of distributing points along a curve is considered. It is assumed that the curve is defined parametrically. The objective is to select a set of parameter values so that the corresponding points on the curves are properly distributed. The distribution is based on some intrinsic property of the curve such as arc length or curvature

Fast carry accumulator design

Simple iterative accumulator combined with gated-carry, carry-completion detection, and skip-carry circuits produces three accumulators with decreased carry propagation times. Devices are used in machine control, measurement equipment, and computer applications to increase speed of binary addition. NAND gates are used in combining network

Errors in finite-difference computations on curvilinear coordinate systems

Curvilinear coordinate systems were used extensively to solve partial differential equations on arbitrary regions. An analysis of truncation error in the computation of derivatives revealed why numerical results may be erroneous. A more accurate method of computing derivatives is presented

Elliptic systems and numerical transformations

Properties of a transformation method, which was developed for solving fluid dynamic problems on general two dimensional regions, are discussed. These include construction error of the transformation and applications to mesh generation. An error and stability analysis for the numerical solution of a model parabolic problem is also presented

Quasiconformal mappings and grid generation

A finite difference scheme is developed for constructing quasiconformal mappings for arbitrary simply and doubly connected regions. Computational grids are generated to reduce elliptic equations to canonical form. Examples of conformal mappings on surfaces are also included

Transformation of two and three-dimensional regions by elliptic systems

Finite difference methods for composite grids were analyzed. It was observed that linear interpolation between grids would suffice only where low order accuracy was required. In the context of fluid flow, this would be in regions where the flow was essentially free stream. Higher order interpolation schemes were also investigated. The well known quadratic and cubic interpolating polynomials would increase the formal accuracy of the overall numerical algorithm. However, it can also be shown that the stability of the algorithm may be adversely affected. Further numerical results are needed in order to assess the nature of this instability induced by the interpolation procedure. Finally, error analysis and the order of difference expressions on general curvilinear coordinates are discussed

A simple dead-reckoning navigational system

Simple navigation system is designed for vehicles operating in remote locations where it is not feasible to transport extensive equipment. System consists of four main components: directional gyrocompass to establish inertial direction; odometer to measure distance; signal processor to combine measured distance and direction; and sun compass to determine initial direction

Adaptive EAGLE dynamic solution adaptation and grid quality enhancement

In the effort described here, the elliptic grid generation procedure in the EAGLE grid code was separated from the main code into a subroutine, and a new subroutine which evaluates several grid quality measures at each grid point was added. The elliptic grid routine can now be called, either by a computational fluid dynamics (CFD) code to generate a new adaptive grid based on flow variables and quality measures through multiple adaptation, or by the EAGLE main code to generate a grid based on quality measure variables through static adaptation. Arrays of flow variables can be read into the EAGLE grid code for use in static adaptation as well. These major changes in the EAGLE adaptive grid system make it easier to convert any CFD code that operates on a block-structured grid (or single-block grid) into a multiple adaptive code

The Shapes of Tight Composite Knots

We present new computations of tight shapes obtained using the constrained gradient descent code RIDGERUNNER for 544 composite knots with 12 and fewer crossings, expanding our dataset to 943 knots and links. We use the new data set to analyze two outstanding conjectures about tight knots, namely that the ropelengths of composite knots are at least 4\pi-4 less than the sums of the prime factors and that the writhes of composite knots are the sums of the writhes of the prime factors.Comment: Summary text file of tight knot lengths and writhing numbers stored in anc/ropelength_data.txt. All other data freely available at http:://www.jasoncantarella.com/ and through Data Conservanc