Multi-Dimensional ENO Schemes for General Geometries

A class of ENO schemes is presented for the numerical solution of multidimensional hyperbolic systems of conservation laws in structured and unstructured grids. This is a class of shock-capturing schemes which are designed to compute cell-averages to high order accuracy. The ENO scheme is composed of a piecewise-polynomial reconstruction of the solution form its given cell-averages, approximate evolution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is based on an adaptive selection of stencil for each cell so as to avoid spurious oscillations near discontinuities while achieving high order of accuracy away from them

On the application and extension of Harten's high resolution scheme

Extensions of a second order high resolution explicit method for the numerical computation of weak solutions of one dimensonal hyperbolic conservation laws are discussed. The main objectives were (1) to examine the shock resoluton of Harten's method for a two dimensional shock reflection problem, (2) to study the use of a high resolution scheme as a post-processor to an approximate steady state solution, and (3) to construct an implicit in the delta-form using Harten's scheme for the explicit operator and a simplified iteration matrix for the implicit operator

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme

Uniformly high order accurate essentially non-oscillatory schemes 3

In this paper (a third in a series) the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws are presented. Also presented is a hierarchy of high order accurate schemes which generalizes Godunov's scheme and its second order accurate MUSCL extension to arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear

Polarization Modeling and Predictions for DKIST Part 2: Application of the Berreman Calculus to Spectral Polarization Fringes of Beamsplitters and Crystal Retarders

We outline polarization fringe predictions derived from a new application of the Berreman calculus for the Daniel K. Inouye Solar Telescope (DKIST) retarder optics. The DKIST retarder baseline design used 6 crystals, single-layer anti-reflection coatings, thick cover windows and oil between all optical interfaces. This new tool estimates polarization fringes and optic Mueller matrices as functions of all optical design choices. The amplitude and period of polarized fringes under design changes, manufacturing errors, tolerances and several physical factors can now be estimated. This tool compares well with observations of fringes for data collected with the SPINOR spectropolarimeter at the Dunn Solar Telescope using bi-crystalline achromatic retarders as well as laboratory tests. With this new tool, we show impacts of design decisions on polarization fringes as impacted by anti-reflection coatings, oil refractive indices, cover window presence and part thicknesses. This tool helped DKIST decide to remove retarder cover windows and also recommends reconsideration of coating strategies for DKIST. We anticipate this tool to be essential in designing future retarders for mitigation of polarization and intensity fringe errors in other high spectral resolution astronomical systems.Comment: Accepted for publication in JATI

Debating Privacy and ICT: Amsterdam January 17, 2002

Conference repor

Representations of world coordinates in FITS

The initial descriptions of the FITS format provided a simplified method for describing the physical coordinate values of the image pixels, but deliberately did not specify any of the detailed conventions required to convey the complexities of actual image coordinates. Building on conventions in wide use within astronomy, this paper proposes general extensions to the original methods for describing the world coordinates of FITS data. In subsequent papers, we apply these general conventions to the methods by which spherical coordinates may be projected onto a two-dimensional plane and to frequency/wavelength/velocity coordinates.Comment: 15 Pages, 1 figure, LaTex with Astronomy & Astrophysics macro package, submitted to A&A, related papers at http://www.aoc.nrao.edu/~egreise

An open and parallel multiresolution framework using block-based adaptive grids

A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and explicit time integration. Grid refinement and coarsening are triggered by multiresolution analysis, i.e. thresholding of wavelet coefficients, which allow controlling the precision of the adaptive approximation of the solution with respect to uniform grid computations. The implementation of the scheme is fully parallel using MPI with a hybrid data structure. Load balancing relies on space filling curves techniques. Validation tests for 2D advection equations allow to assess the precision and performance of the developed code. Computations of the compressible Navier-Stokes equations for a temporally developing 2D mixing layer illustrate the properties of the code for nonlinear multi-scale problems. The code is open source

A search for H₂ emission in bipolar nebulae and regions of interstellar shock

We report a H2 emission survey of five bipolar outflow sources (NGC 1333, M2-9, As 353, S106, V645 Cyg), and one region of shock interaction between an H II region and molecular cloud (NGC 281). Two of the sources (M2-9, NGC 1333) were detected in the v = 1-0S(1), and Q-branch transitions of H2, and we provide a detailed analysis and modelling for these cases. The probable mass of shocked H2 is shown to range between 1.4 10-6 and 4.2 10-8 M⊙ for M2-9, and ≈ 2.5-4 and 1.9-10 M⊙ in the case of NGC 1333, although the latter values may require increasing by a factor of a few when due allowance is made for extinction. A detailed analysis for the core of M2-9 indicates that the ionized zone is extremely compact, and our Brackett line measures support other evidence in suggesting a high core extinction, large emission measure E~4 1010 cm-6 pc, and a projected angular radius θc~0.04. Similarly, it is apparent from the H2S(1) line strength that the core expansion velocity must be low and less than ~ 1 km s-1 (a constraint which is also required on dynamical grounds). Finally, CO J = 3-2 observations of the source failed to detect emission above a 2σ limit of T*R ~ 0.4 K, and this is shown to imply a probable expansion timescale of ≲2 103 yr