ALBERT

Description: Basic algorithms for unstructured mesh generation and fluid flow calculation are discussed. In particular the following are addressed: preliminaries of graphs and meshes; duality and data structures; basic graph operations important in CFD (Computational Fluid Dynamics); triangulation methods, including Varonoi diagrams and Delaunay triangulation; maximum principle analysis; finite volume schemes for scalar conservation law equations; finite volume schemes for the Euler and Navier-Stokes equations; and convergence acceleration for steady state calculations.

Description: Selected results are presented for an analysis of Mariner 9 1304-A data from the first 100 passes. Based on a comparison of limb data, the exospheric temperature appears lower on several Mariner 9 passes than when Mariner 6 and 7 encountered the planet in 1969. Temperatures of 300 and 350 K are considered in the atmospheric modeling. At 300 K, derived values of the atomic oxygen concentration are typically between 0.5 and 1 percent of the total density at 135 km, based on fitting theoretical intensities to limb data from several passes. Structure in the limb data below 200 km suggests the possibility that approximately 0.2 kR of the observed approximately 0.8 kR near 150 km is due to dissociative excitation of CO2. There is variability in limb profiles indicating changes in the O distribution with time. The variability does not appear to follow a recognizable pattern. Interpretation of the 1304-A disc data shows a correlation in intensity with the 10.7 cm solar flux and larger O concentrations in the afternoon than in the morning. The correlation in intensity with the 10.7 cm flux is probably due largely to variation in the solar 1304-A fluxes. Selected disc data show localized and random enhancements in the intensity.

Description: The fundamentals and the state-of-the-art technology for unstructured grids and solvers are highlighted. Algorithms and techniques pertinent to mesh generation are discussed. It is shown that grid generation and grid manipulation schemes rely on fast multidimensional searching. Flow solution techniques for the Euler equations, which can be derived from the integral form of the equations are discussed. Sample calculations are also provided.

Description: We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

Description: This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

Description: The Galileo Extreme Ultraviolet Spectrometer obtained a spectrum of Venus atmospheric emissions in the 55.0- to 125.0-nm wavelength region. Emissions of helium (58.4 nm), ionized atomic oxygen (83.4 nm), and atomic hydrogen (121.6 nm), as well as a blended spectral feature of atomic hydrogen (Lyman-beta) and atomic oxygen (102.5 nm), were observed at 3.5-nm resolution. During the Galileo spacecraft cruise from Venus to earth, Lyman-alpha emission from solar system atomic hydrogen (121.6 nm) was measured. The dominant source of the Lyman-alpha emission is atomic hydrogen from the interstellar medium. A model of Galileo observations at solar maximum indicates a decrease in the solar Lyman-alpha flux near the solar poles. A strong day-to-day variation also occurs with the 27-day periodicity of the rotation of the sun.

Description: Two focused Mars missions that would fit within the guidelines for the proposed Discovery line are discussed. The first mission would deal with the issue of the escape of the atmosphere (Mars') to space. A complete understanding of this topic is crucial to deciphering the evolution of the atmosphere, climate change, and volatile inventories. The second mission concerns the investigation of remanent magnetization of the crust and its relationship to the ionosphere and the atmosphere.

Description: Various topics concerned with the upper atmosphere of the earth and planets are discussed. The atmospheres of the terrestrial planets are addressed, emphasizing Venus. The energy budget of the mesosphere and thermosphere is considered, discussing current and particles as energy sources, the radiation field, and neutral atmosphere dynamics. The results of Pre-Map Project One are covered, and the International Reference Ionosphere is discussed, including electron density profiles, the lower ionosphere, the plasmasphere, plasma temperature profiles, and ion composition. Finally, the mass spectroscopy of atmospheres is treated.

Description: High order accurate finite-volume schemes for solving the Euler equations of gasdynamics are developed. Central to the development of these methods are the construction of a k-exact reconstruction operator given cell-averaged quantities and the use of high order flux quadrature formulas. General polygonal control volumes (with curved boundary edges) are considered. The formulations presented make no explicit assumption as to complexity or convexity of control volumes. Numerical examples are presented for Ringleb flow to validate the methodology.

Description: The role of involutions in energy stability of the discontinuous Galerkin (DG) discretization of Maxwell and magnetohydrodynamic (MHD) systems is examined. Important differences are identified in the symmetrization of the Maxwell and MHD systems that impact the construction of energy stable discretizations using the DG method. Specifically, general sufficient conditions to be imposed on the DG numerical flux and approximation space are given so that energy stability is retained These sufficient conditions reveal the favorable energy consequence of imposing continuity in the normal component of the magnetic induction field at interelement boundaries for MHD discretizations. Counterintuitively, this condition is not required for stability of Maxwell discretizations using the discontinuous Galerkin method.