Anisotropic geometry-conforming d-simplicial meshing via isometric embeddings

We develop a dimension-independent, Delaunay-based anisotropic mesh generation algorithm suitable for integration with adaptive numerical solvers. As such, the mesh produced by our algorithm conforms to an anisotropic metric prescribed by the solver as well as the domain geometry, given as a piecewise smooth complex. Motivated by the work of Lévy and Dassi [10-12,20], we use a discrete manifold embedding algorithm to transform the anisotropic problem to a uniform one. This work differs from previous approaches in several ways. First, the embedding algorithm is driven by a Riemannian metric field instead of the Gauss map, lending itself to general anisotropic mesh generation problems. Second we describe our method for computing restricted Voronoi diagrams in a dimension-independent manner which is used to compute constrained centroidal Voronoi tessellations. In particular, we compute restricted Voronoi simplices using exact arithmetic and use data structures based on convex polytope theory. Finally, since adaptive solvers require geometry-conforming meshes, we offer a Steiner vertex insertion algorithm for ensuring the extracted dual Delaunay triangulation is homeomorphic to the input geometries. The two major contributions of this paper are: a method for isometrically embedding arbitrary mesh-metric pairs in higher dimensional Euclidean spaces and a dimension-independent vertex insertion algorithm for producing geometry-conforming Delaunay meshes. The former is demonstrated on a two-dimensional anisotropic problem whereas the latter is demonstrated on both 3d and 4d problems. Keywords: Anisotropic mesh generation; metric; Nash embedding theorem; isometric; geometry-conforming; restricted Voronoi diagram; constrained centroidal Voronoi tessellation; Steiner vertices; dimension-independen

A Discontinuous Galerkin Chimera scheme

The Chimera overset method is a powerful technique for modeling fluid flow associated with complex engineering problems using structured meshes. The use of structured meshes has enabled engineers to employ a number of high-order schemes, such as the WENO and compact differencing schemes. However, the large stencil associated with these schemes can significantly complicate the inter-grid communication scheme and hole cutting procedures. This paper demonstrates a methodology for using the Discontinuous Galerkin (DG) scheme with Chimera overset meshes. The small stencil of the DG scheme makes it particularly suitable for Chimera meshes as it simplifies the inter-grid communication scheme as well as hole cutting procedures. The DG-Chimera scheme does not require a donor interpolation method with a large stencil because the DG scheme represents the solution as cell local polynomials. The DG-Chimera method also does not require the use of fringe points to maintain the interior stencil across inter-grid boundaries. Thus, inter-grid communication can be established as long as the receiving boundary is enclosed by or abuts the donor mesh. This makes the inter-grid communication procedure applicable to both Chimera and zonal meshes. Details of the DG-Chimera scheme are presented, and the method is demonstrated on a set of two-dimensional inviscid flow problems

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations

Introduction to COFFE: The Next-Generation HPCMP CREATE-AV CFD Solver

HPCMP CREATE-AV Conservative Field Finite Element (COFFE) is a modular, extensible, robust numerical solver for the Navier-Stokes equations that invokes modularity and extensibility from its first principles. COFFE implores a flexible, class-based hierarchy that provides a modular approach consisting of discretization, physics, parallelization, and linear algebra components. These components are developed with modern software engineering principles to ensure ease of uptake from a user's or developer's perspective. The Streamwise Upwind/Petrov-Galerkin (SU/PG) method is utilized to discretize the compressible Reynolds-Averaged Navier-Stokes (RANS) equations tightly coupled with a variety of turbulence models. The mathematics and the philosophy of the methodology that makes up COFFE are presented

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. Laminar flow over a delta wing is verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and pitching moment

Recent variability of the global ocean carbon sink

We present a new observation-based estimate of the global oceanic carbon dioxide (CO2) sink and its temporal variation on a monthly basis from 1998 through 2011 and at a spatial resolution of 1×1. This sink estimate rests upon a neural network-based mapping of global surface ocean observations of the partial pressure of CO2 (pCO2) from the Surface Ocean CO2 Atlas database. The resulting pCO2 has small biases when evaluated against independent observations in the different ocean basins, but larger randomly distributed differences exist particularly in high latitudes. The seasonal climatology of our neural network-based product agrees overall well with the Takahashi et al. (2009) climatology, although our product produces a stronger seasonal cycle at high latitudes. From our global pCO2 product, we compute a mean net global ocean (excluding the Arctic Ocean and coastal regions) CO2 uptake flux of −1.42 ± 0.53 Pg C yr−1, which is in good agreement with ocean inversion-based estimates. Our data indicate a moderate level of interannual variability in the ocean carbon sink (±0.12 Pg C yr−1, 1𝜎) from 1998 through 2011, mostly originating from the equatorial Pacific Ocean, and associated with the El Nino–Southern Oscillation. Accounting for steady state riverine and Arctic Ocean carbon fluxes our estimate further implies a mean anthropogenic CO2 uptake of −1.99 ± 0.59 Pg C yr−1 over the analysis period. From this estimate plus the most recent estimates for fossil fuel emissions and atmospheric CO2 accumulation, we infer a mean global land sink of −2.82 ± 0.85 Pg C yr−1 over the 1998 through 2011 period with strong interannual variation

Agency, stewardship and the universal-family firm : a qualitative historical analysis

This paper introduces the idea of a non-kinship-based Universal-family firm, an organizational form we developed based on interpreting historical writings in their socio-economic context. We analyzed Luke’s gospel with an eye toward drawing implications for the stewardship-agency debate in the contemporary family business literature. Our paper makes contributions at two important levels. In addition to introducing and developing theory about the Universal-family firms, we also contribute to the methodological toolkit of family business scholars by providing a template for using historical documents to challenge, enhance and develop theory

Extratropical forcing and tropical rainfall distribution: energetics framework and ocean Ekman advection

Intense tropical rainfall occurs in a narrow belt near the equator, called the inter-tropical convergence zone (ITCZ). In the past decade, the atmospheric energy budget has been used to explain changes in the zonal-mean ITCZ position. The energetics framework provides a mechanism for extratropics-to-tropics teleconnections, which have been postulated from paleoclimate records. In atmosphere models coupled with a motionless slab ocean, the ITCZ shifts toward the warmed hemisphere in order for the Hadley circulation to transport energy toward the colder hemisphere. However, recent studies using fully coupled models show that tropical rainfall can be rather insensitive to extratropical forcing when ocean dynamics is included. Here, we explore the effect of meridional Ekman heat advection while neglecting the upwelling effect on the ITCZ response to prescribed extratropical thermal forcing. The tropical component of Ekman advection is a negative feedback that partially compensates the prescribed forcing, whereas the extratropical component is a positive feedback that amplifies the prescribed forcing. Overall, the tropical negative feedback dominates over the extratropical positive feedback. Thus, including Ekman advection reduces the need for atmospheric energy transport, dampening the ITCZ response. We propose to build a hierarchy of ocean models to systematically explore the full dynamical response of the coupled climate system