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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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11 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2023

Evaluation of Voronoi Meshes for Large Eddy Simulations of High Lift Aerodynamics

Numerical sensitivity to 3 different Voronoi seeding methods is investigated for Large Eddy Simulations (LES). A second order accurate, non-dissipative finite volume discretization is used to systematically investigate the effects of different polyhedral Voronoi mesh types using a sequence of three canonical problems with increasing complexity. First, inviscid isentropic vortex propagation is studied to demonstrate the substantial reduction of errors for rhombic dodecahedron and truncated octahedral cell types over Cartesian hexagonal cells of identical spacing. Furthermore, the reduction of errors induced at cell-size transitions (grid-coarsening interfaces) due to Lloyd smoothing iterations is quantified. It is shown that by utilizing an appropriate viscous flux discretization, a constant coefficient subgrid scale model is sufficient for non-linear stability at the 2:1 cell-size transitions on polyhedral grids, although some further error reduction does occur when smoothing is utilized. Next, forced homogeneous isotropic turbulence at an asymptotically large Reynolds number is studied to demonstrate the non-dissipative character of the inviscid flux discretization, and the non-linear robustness and accuracy offered by the viscous flux discretization using a subgrid scale model for all three Voronoi grid types. Finally,Wall-Modeled Large Eddy Simulations (WMLES) are performed to study the high-lift aerodynamics on the McDonnell Douglas 30P30N multi-element airfoil at two distinct grid levels and for two distinct Voronoi cell types. The formulation is shown to predict the aerodynamic loading with high accuracy at all angles of attack when sufficient resolution is reached, and the hexagonal prism grid topology, while computationally more expensive, has higher effective resolution compared to the Cartesian grid topology with the same spacing.

TTT↗
NASA NTRS2023

Evaluation of Voronoi Meshes for Large Eddy Simulations of High Lift Aerodynamics

Numerical sensitivity to 3 different Voronoi seeding methods is investigated for Large Eddy Simulations (LES). A second order accurate, non-dissipative finite volume discretization is used to systematically investigate the effects of different polyhedral Voronoi mesh types using a sequence of three canonical problems with increasing complexity. First, inviscid isentropic vortex propagation is studied to demonstrate the substantial reduction of errors for rhombic dodecahedron and truncated octahedral cell types over Cartesian hexagonal cells of identical spacing. Furthermore, the reduction of errors induced at cell-size transitions (grid-coarsening interfaces) due to Lloyd smoothing iterations is quantified. It is shown that by utilizing an appropriate viscous flux discretization, a constant coefficient subgrid scale model is sufficient for non-linear stability at the 2:1 cell-size transitions on polyhedral grids, although some further error reduction does occur when smoothing is utilized. Next, forced homogeneous isotropic turbulence at an asymptotically large Reynolds number is studied to demonstrate the non-dissipative character of the inviscid flux discretization, and the non-linear robustness and accuracy offered by the viscous flux discretization using a subgrid scale model for all three Voronoi grid types. Finally, Wall-Modeled Large Eddy Simulations (WMLES) are performed to study the high-lift aerodynamics on the McDonnell Douglas 30P30N multi-element airfoil at two distinct grid levels and for two distinct Voronoi cell types. The formulation is shown to predict the aerodynamic loading with high accuracy at all angles of attack when sufficient resolution is reached, and the hexagonal prism grid topology, while computationally more expensive, has higher effective resolution compared to the Cartesian grid topology with the same spacing.

TTT↗
NASA NTRS2017

JIGSAW-GEO (1.0): Locally Orthogonal Staggered Unstructured Grid Generation for General Circulation Modelling on the Sphere

An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered VoronoiDelaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

geophysical fluid dynamics↗
NASA NTRS1985

Three-dimensional algorithms for grid restructuring in Free-Lagrangian calculations

Grid restructuring algorithms which lower the price of three-dimensional Free-Lagrange calculations are presented. The algorithms are first given for the case of planar triangulated surfaces embedded in and spanning a three-dimensional region. The tetrahedra generated by this technique form a Delaunay mesh if the interplane spacing is comparable to the resolution within the planes. The algorithm can therefore be used for efficient determinations of Voronoi connections for initial grids. Modifications of the algorithm for the case of closely spaced surfaces are demonstrated in the context of restructuring algorithms which can accommodate colliding surfaces. Then, the restriction to planar surfaces is removed and regular surfaces are examined. The basic algorithm is the same, with an additional operation to project the vertices of one surface onto another. Finally, vertices on the surface are allowed to migrate anywhere in space.

Fritts, M.↗
NASA NTRS2015

Multi-Resolution Unstructured Grid-Generation for Geophysical Applications on the Sphere

An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric and ocean simulation, and numerical weather predication. Using a recently developed Frontal-Delaunay-refinement technique, a method for the construction of high-quality unstructured ellipsoidal Delaunay triangulations is introduced. A dual polygonal grid, derived from the associated Voronoi diagram, is also optionally generated as a by-product. Compared to existing techniques, it is shown that the Frontal-Delaunay approach typically produces grids with near-optimal element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform ellipsoidal grids appropriate for large-scale geophysical applications. The use of user-defined mesh-sizing functions to generate smoothly graded, non-uniform grids is discussed.

Weather↗
NASA NTRS1988

Discretization formulas for unstructured grids

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formula in cartesian coordinates for the Laplacian operator, first derivative operators and the function for unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator are shown to agree with the Taylor series approach on a global average. In addition, a simple algorithm is presented to determine the Voronoi (finite difference) area of an unstructured grid.

Baumeister, Kenneth J.↗
NASA NTRS1988

Discretization formulas for unstructured grids

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formula in cartesian coordinates for the Laplacian operator, first derivative operators and the function for unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator are shown to agree with the Taylor series approach on a global average. In addition, a simple algorithm is presented to determine the Voronoi (finite difference) area of an unstructured grid.

Baumeister, Kenneth J.↗
NASA NTRS2018

Generalised Primal-Dual Grids for Unstructured Co-Volume Schemes

The generation of high-quality staggered unstructured grids is considered, leading to the development of a new optimisation-based strategy designed to construct weighted 'Regular-Power' tessellations appropriate for co-volume type numerical discretisation techniques. This new framework aims to extend the conventional Delaunay-Voronoi primal-dual structure; seeking to assemble generalised orthogonal tessellations with enhanced geometric quality. The construction of these grids is motivated by the desire to improve the performance and accuracy of numerical methods based on unstructured co-volume type schemes, including various staggered grid techniques for the simulation of fluid dynamics and hyperbolic transport. In this study, a new hybrid optimisation strategy is proposed; seeking to optimise the geometry, topology and weights associated with general, two-dimensional Regular-Power tessellations using a combination of gradient-ascent and energy-based techniques. The performance of this new method is tested experimentally, with a range of complex, multi-resolution primal-dual grids generated for various coastal and regional ocean modelling applications.

power diagrams↗
NASA NTRS2000

Interference Lattice-based Loop Nest Tilings for Stencil Computations

A common method for improving performance of stencil operations on structured multi-dimensional discretization grids is loop tiling. Tile shapes and sizes are usually determined heuristically, based on the size of the primary data cache. We provide a lower bound on the numbers of cache misses that must be incurred by any tiling, and a close achievable bound using a particular tiling based on the grid interference lattice. The latter tiling is used to derive highly efficient loop orderings. The total number of cache misses of a code is the sum of (necessary) cold misses and misses caused by elements being dropped from the cache between successive loads (replacement misses). Maximizing temporal locality is equivalent to minimizing replacement misses. Temporal locality of loop nests implementing stencil operations is optimized by tilings that avoid data conflicts. We divide the loop nest iteration space into conflict-free tiles, derived from the cache miss equation. The tiling involves the definition of the grid interference lattice an equivalence class of grid points whose images in main memory map to the same location in the cache-and the construction of a special basis for the lattice. Conflicts only occur on the boundaries of the tiles, unless the tiles are too thin. We show that the surface area of the tiles is bounded for grids of any dimensionality, and for caches of any associativity, provided the eccentricity of the fundamental parallelepiped (the tile spanned by the basis) of the lattice is bounded. Eccentricity is determined by two factors, aspect ratio and skewness. The aspect ratio of the parallelepiped can be bounded by appropriate array padding. The skewness can be bounded by the choice of a proper basis. Combining these two strategies ensures that pathologically thin tiles are avoided. They do not, however, minimize replacement misses per se. The reason is that tile visitation order influences the number of data conflicts on the tile boundaries. If two adjacent tiles are visited successively, there will be no replacement misses on the shared boundary. The iteration space may be covered with pencils larger than the size of the cache while avoiding data conflicts if the pencils are traversed by a scanning-face method. Replacement misses are incurred only on the boundaries of the pencils, and the number of misses is minimized by maximizing the volume of the scanning face, not the volume of the tile. We present an algorithm for constructing the most efficient scanning face for a given grid and stencil operator. In two dimensions it is based on a continued fraction algorithm. In three dimensions it follows Voronoi's successive minima algorithm. We show experimental results of using the scanning face, and compare with canonical loop orderings.

VanderWijngaart, Rob F.↗
NASA NTRS1995

Algorithms for high aspect ratio oriented triangulations

Grid generation plays an integral part in the solution of computational fluid dynamics problems for aerodynamics applications. A major difficulty with standard structured grid generation, which produces quadrilateral (or hexahedral) elements with implicit connectivity, has been the requirement for a great deal of human intervention in developing grids around complex configurations. This has led to investigations into unstructured grids with explicit connectivities, which are primarily composed of triangular (or tetrahedral) elements, although other subdivisions of convex cells may be used. The existence of large gradients in the solution of aerodynamic problems may be exploited to reduce the computational effort by using high aspect ratio elements in high gradient regions. However, the heuristic approaches currently in use do not adequately address this need for high aspect ratio unstructured grids. High aspect ratio triangulations very often produce the large angles that are to be avoided. Point generation techniques based on contour or front generation are judged to be the most promising in terms of being able to handle complicated multiple body objects, with this technique lending itself well to adaptivity. The eventual goal encompasses several phases: first, a partitioning phase, in which the Voronoi diagram of a set of points and line segments (the input set) will be generated to partition the input domain; second, a contour generation phase in which body-conforming contours are used to subdivide the partition further as well as introduce the foundation for aspect ratio control, and; third, a Steiner triangulation phase in which points are added to the partition to enable triangulation while controlling angle bounds and aspect ratio. This provides a combination of the advancing front/contour techniques and refinement. By using a front, aspect ratio can be better controlled. By using refinement, bounds on angles can be maintained, while attempting to minimize the number of Steiner points.

Posenau, Mary-Anne K.↗
NASA NTRS2015

Voronoi-Based Point-Placement for Three-Dimensional Delaunay-Refinement

An extension of the restricted Delaunay-refinement algorithm for three-dimensional tetrahedral mesh generation is described, in which an off-centre type point-placement scheme is utilised. It is shown that the use of generalised Steiner points, positioned along edges in the associated Voronoi complex, typically leads to improvements in the overall size, quality and grading of the resulting tetrahedral meshes. The new algorithm can be viewed as a Frontal-Delaunay approach - a hybridisation of conventional Delaunay-refinement and advancing-front techniques, in which new vertices are positioned to satisfy both element size- and shapeconstraints. The new method is shown to inherit many of the best features of classical Delaunay-refinement and advancing-front type algorithms, combining good practical performance with theoretical robustness. Experimental comparisons show that

algorithms↗