Face- and Cell-Averaged Nodal-Gradient Approach to Cell-Centered Finite-Volume Method on Mixed Grids

In this paper, the averaged nodal-gradient approach previously developed for triangular grids is extended to mixed triangular-quadrilateral grids. It is shown that the face- averaged approach leads to deteriorated iterative convergence on quadrilateral grids. To develop a convergent solver, we consider cell-averaging instead of face-averaging for quadri- lateral cells. We show that the cell-averaged approach leads to a convergent solver and can be efficiently combined with the face-averaged approach on mixed grids. The method is demonstrated for various inviscid and viscous problems from low to high Mach numbers on two-dimensional mixed grids

Efficient and Robust Weighted Least-Squares Cell-Average Gradient Construction Methods for the Simulation of Scramjet Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. The construction of cell-average gradients using a weighted linear least-squares method and the use of these gradients in the construction of the inviscid fluxes is the focus of this paper. A comparison of least-squares stencil construction methodologies is presented and approaches designed to minimize the number of cells used to augment/stabilize the least-squares stencil while preserving accuracy are explored. Due to our interest in hypersonic flow, a robust multidimensional cell-average gradient limiter procedure that is consistent with the stencil used to construct the cellaverage gradients is described. Canonical problems are computed to illustrate the challenges and investigate the accuracy, robustness and convergence behavior of the cell-average gradient methods on unstructured cell-centered finite-volume grids. Finally, thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet engine flowpath is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the preferred gradient method for a realistic 3-D geometry on a non-hex-dominant grid

An Efficient Quadratic Interpolation Scheme for a Third-Order Cell-Centered Finite-Volume Method on Tetrahedral Grids

In this paper, we propose an efficient quadratic interpolation formula utilizing solution gradients computed and stored at nodes and demonstrate its application to a third-order cell-centered finite-volume discretization on tetrahedral grids. The proposed quadratic formula is constructed based on an efficient formula of computing a projected derivative. It is efficient in that it completely eliminates the need to compute and store second derivatives of solution variables or any other quantities, which are typically required in upgrading a second-order cell-centered unstructured-grid finite-volume discretization to third-order accuracy. Moreover, a high-order flux quadrature formula, as required for third-order accuracy, can also be simplified by utilizing the efficient projected-derivative formula, resulting in a numerical flux at a face centroid plus a curvature correction not involving second derivatives of the flux. Similarly, a source term can be integrated over a cell to high-order in the form of a source term evaluated at the cell centroid plus a curvature correction, again, not requiring second derivatives of the source term. The discretization is defined as an approximation to an integral form of a conservation law but the numerical solution is defined as a point value at a cell center, leading to another feature that there is no need to compute and store geometric moments for a quadratic polynomial to preserve a cell average. Third-order accuracy and improved second-order accuracy are demonstrated and investigated for simple but illustrative test cases in three dimensions

Analysis of Instabilities in Non-Axisymmetric Hypersonic Boundary Layers Over Cones

Hypersonic flows over circular cones constitute one of the most important generic configurations for fundamental aerodynamic and aerothermodynamic studies. In this paper, numerical computations are carried out for Mach 6 flows over a 7-degree half-angle cone with two different flow incidence angles and a compression cone with a large concave curvature. Instability wave and transition-related flow physics are investigated using a series of advanced stability methods ranging from conventional linear stability theory (LST) and a higher-fidelity linear and nonlinear parabolized stability equations (PSE), to the 2D eigenvalue analysis based on partial differential equations. Computed N factor distribution pertinent to various instability mechanisms over the cone surface provides initial assessments of possible transition fronts and a guide to corresponding disturbance characteristics such as frequency and azimuthal wave numbers. It is also shown that strong secondary instability that eventually leads to transition to turbulence can be simulated very efficiently using a combination of advanced stability methods described above

Secondary Instability of Second Modes in Hypersonic Boundary Layers

Second mode disturbances dominate the primary instability stage of transition in a number of hypersonic flow configurations. The highest amplification rates of second mode disturbances are usually associated with 2D (or axisymmetric) perturbations and, therefore, a likely scenario for the onset of the three-dimensionality required for laminar-turbulent transition corresponds to the parametric amplification of 3D secondary instabilities in the presence of 2D, finite amplitude second mode disturbances. The secondary instability of second mode disturbances is studied for selected canonical flow configurations. The basic state for the secondary instability analysis is obtained by tracking the linear and nonlinear evolution of 2D, second mode disturbances using nonlinear parabolized stability equations. Unlike in previous studies, the selection of primary disturbances used for the secondary instability analysis was based on their potential relevance to transition in a low disturbance environment and the effects of nonlinearity on the evolution of primary disturbances was accounted for. Strongly nonlinear effects related to the self-interaction of second mode disturbances lead to an upstream shift in the upper branch neutral location. Secondary instability computations confirm the previously known dominance of subharmonic modes at relatively small primary amplitudes. However, for the Purdue Mach 6 compression cone configuration, it was shown that a strong fundamental secondary instability can exist for a range of initial amplitudes of the most amplified second mode disturbance, indicating that the exclusive focus on subharmonic modes in the previous applications of secondary instability theory to second mode primary instability may not have been fully justified

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and efficiency are studied for six nominally second-order accurate schemes: a node-centered scheme, cell-centered node-averaging schemes with and without clipping, and cell-centered schemes with unweighted, weighted, and approximately mapped least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Results from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The second class of tests are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes are less accurate, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to the complexity of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping of the surface anisotropy or modifying the scheme stencil to reflect the direction of strong coupling

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Viscous Fluxes

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered scheme and three cell-centered schemes - a node-averaging scheme and two schemes with nearest-neighbor and adaptive compact stencils for least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Tests from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The tests of the second class are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes may degenerate on mixed grids, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to that of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping based on a distance function commonly available in practical schemes or modifying the scheme stencil to reflect the direction of strong coupling. The major conclusion is that accuracies of the node centered and the best cell-centered schemes are comparable at equivalent number of degrees of freedom

The Influence of Operational Resources and Activities on Indirect Personnel Costs: A Multilevel Modeling Approach

Indirect activities often represent an underemphasized, yet significant, contributing source of costs for organizations. In order to manage indirect costs, organizations must understand how these costs behave relative to changes in operational resources and activities. This is of particular interest to the Air Force and its sister services, because recent and projected reductions in defense spending are forcing reductions in their operational variables, and insufficient research exists to help them understand how this may influence indirect costs. Furthermore, although academic research on indirect costs has advanced the knowledge behind the modeling and behavior of indirect costs, significant gaps in the literature remain. Our research provides important and timely advances to the indirect cost literature. First, our research disaggregates the indirect cost pool and focuses on indirect personnel costs, which represent 33% of all Air Force indirect costs and are a leading source of indirect costs in many organizations. Second, we employ a multilevel modeling approach to capture the hierarchical nature of an enterprise, allowing us to assess the influence that each level of an organization has on indirect cost behavior and relationships. Third, we identify the operational variables that influence indirect personnel costs in the Air Force enterprise, providing Air Force decision-makers with evidence-based knowledge to inform decisions regarding budget reduction strategies

The MultiSite Spectroscopic Telescope campaign: 2m spectroscopy of the V361 Hya variable PG1605+072

We present results and analysis for the 2m spectroscopic part of the MultiSite Spectroscopic Telescope (MSST) campaign undertaken in May/June 2002. The goal of the project was to observe the pulsating subdwarf B star PG1605+072 simultaneously in velocity and photometry and to resolve as many of the >50 known modes as possible, which will allow a detailed asteroseismological analysis. We have obtained over 150 hours of spectroscopy, leading to an unprecedented noise level of only 207m/s. We report here the detection of 20 frequencies in velocity, with two more likely just below our detection threshold. In particular, we detect 6 linear combinations, making PG1605+072 only the second star known to show such frequencies in velocity. We investigate the phases of these combinations and their parent modes and find relationships between them that cannot be easily understood based on current theory. These observations, when combined with our simultaneous photometry, should allow asteroseismology of this most complicated of sdB pulsators.Comment: 9 pages, 5 figures, accepted for publication in A&A; Figure 1 at lower resolution than accepted versio

Photosynthetic Characteristics of \u3ci\u3eVeratrum californicum\u3c/i\u3e in Varied Greenhouse Environments

Corn lily or California false hellebore (Veratrum californicum Durand), a perennial species native to the western United States, produces several alkaloid compounds. A derivative of these alkaloid compounds, primarily veratramine and cyclopamine, shows promise as a therapeutic agent for treatment of a variety of tumor types. Here we report the first study of corn lily cultivated in greenhouse. Growth response of corn lily was examined under two light levels (ambient and supplemental), two fertilization types (20 N-4.4 P-16.6 K Peat-lite special and 15N-2.2P-12.5K CalMag special) at 100-mg·L-1 total nitrogen, and three irrigation cycles [sub-irrigation every day (wet), every third day (dry), and hand watering]. Net CO2 assimilation rate (Pn) and transpiration rate (ET) of corn lily grown under supplemental light were 11.0% and 44.7%, respectively, higher than those under ambient light. The Pn and ET of corn lily grown with the wet irrigation cycle increased by 15.2% and 29.4%, respectively, when compared with the Pn and ET of plants grown under the dry irrigation cycle. Corn lily grown wet with supplemental light had the highest average Pn of 8.55 ± 0.36 μmol·m-2·s -1, while plants grown under ambient light with hand watering had the lower average Pn of 6.52 ± 0.48 μmol·m-2·s -1. The highest mean ET recorded for corn lily was 4.97 ± 0.17 mmol·m-2·s -1 when plants were grown dry with supplemental light, while the lowest ET recorded was 2.51 ± 0.18 mmol m-2 s-1 when plants were grown under ambient light and hand with supplemental light and when volumetric water content remained above 44%. The water use efficiency of corn lily may be low, as water is not normally limiting in the natural environment where corn lily grows