Meshing Deforming Spacetime for Visualization and Analysis

We introduce a novel paradigm that simplifies the visualization and analysis of data that have a spatially/temporally varying frame of reference. The primary application driver is tokamak fusion plasma, where science variables (e.g., density and temperature) are interpolated in a complex magnetic field-line-following coordinate system. We also see a similar challenge in rotational fluid mechanics, cosmology, and Lagrangian ocean analysis; such physics implies a deforming spacetime and induces high complexity in volume rendering, isosurfacing, and feature tracking, among various visualization tasks. Without loss of generality, this paper proposes an algorithm to build a simplicial complex -- a tetrahedral mesh, for the deforming 3D spacetime derived from two 2D triangular meshes representing consecutive timesteps. Without introducing new nodes, the resulting mesh fills the gap between 2D meshes with tetrahedral cells while satisfying given constraints on how nodes connect between the two input meshes. In the algorithm we first divide the spacetime into smaller partitions to reduce complexity based on the input geometries and constraints. We then independently search for a feasible tessellation of each partition taking nonconvexity into consideration. We demonstrate multiple use cases for a simplified visualization analysis scheme with a synthetic case and fusion plasma applications

Parallel local mesh refinement for Code Saturne

Computational Fluid Dynamics (CFD) is one of the eld which can fully utilize the capacity of existing HPC systems. There are many cases either from basic or applied research which are so complex that their numerical simulation with requested accuracy requires very ne representation of the computational domain. To solve certain problems numerical models consisting of hundred billions of cells are necessary. There are several approaches to create such huge meshes. One of them is based on global mesh re nement and is also known as mesh multiplication. This approach was already described in [1, 2]. Global re nement was already implemented into Code Saturne enhancing its capability in terms of mesh re nement. Meshes with sizes of up to one hundred billion of cells were generated on the y. Since there are many CFD problems where only local area is of interest (either areas close to boundaries, small geometrical entities or in regions with high gradient of solved quantities), local re nement is another approach for mesh creation. In this paper implementation of parallel local re nement applied to Code Saturne is described. The bottleneck of local adaptive re nement is that it breaks load balancing of the original mesh and requires a lot of global communications. Strategy to re-partition the mesh before its re nement is a key issue for optimal resource utilization. To minimize the amount of data transferred among cores it is necessary to do most of the communication during the preprocessing step on the coarse mesh before re nement. Local mesh re nement strategy was tested and its scalability and performance within Code Saturne were analysed. Results are presented in this paper

ICASE/LaRC Workshop on Adaptive Grid Methods

Solution-adaptive grid techniques are essential to the attainment of practical, user friendly, computational fluid dynamics (CFD) applications. In this three-day workshop, experts gathered together to describe state-of-the-art methods in solution-adaptive grid refinement, analysis, and implementation; to assess the current practice; and to discuss future needs and directions for research. This was accomplished through a series of invited and contributed papers. The workshop focused on a set of two-dimensional test cases designed by the organizers to aid in assessing the current state of development of adaptive grid technology. In addition, a panel of experts from universities, industry, and government research laboratories discussed their views of needs and future directions in this field

A one point integration rule over star convex polytopes

In this paper, the recently proposed linearly consistent one point integration rule for the meshfree methods is extended to arbitrary polytopes. The salient feature of the proposed technique is that it requires only one integration point within each n-sided polytope as opposed to 3n in Francis et al. (2017) and 13n integration points in the conventional approach for numerically integrating the weak form in two dimensions. The essence of the proposed technique is to approximate the compatible strain by a linear smoothing function and evaluate the smoothed nodal derivatives by the discrete form of the divergence theorem at the geometric center. This is done by Taylor's expansion of the weak form which facilitates the use of the smoothed nodal derivatives acting as the stabilization term. This translates to 50% and 30% reduction in the overall computational time in the two and three dimensions, respectively, whilst preserving the accuracy and the convergence rates. Th

Fully anisotropic split-tree adaptive refinement mesh generation using tetrahedral mesh stitching

Due to the myriad of geometric topologies that modern computational fluid dynamicists desire to mesh and run solutions on, the need for a robust Cartesian Mesh Generation algorithm is paramount. Not only do Cartesian meshes require less elements and often help resolve flow features but they also allow the grid generator to have a great deal of control in so far as element aspect ratio, size, and gradation. Fully Anisotropic Split-Tree Adaptive Refinement (FASTAR) is a code that allows the user to exert a great deal of control and ultimately generate a valid, geometry conforming mesh. Due to the split-tree nature and the use of volumetric pixels (voxels), non-unit aspect ratio meshing is easily achieved. Nodes are not generated until the end which mitigates tolerance issues. The tree is retained coherently, and viscous layers may be inserted in the space between the geometry and the Cartesian mesh before it is tetrahedralized. FASTAR uses tree traversal to determine neighbors robustly, and with the tetrahedralization of only a small amount of space around the geometry, sliver cells and inverted elements are avoided. The code uses Riemannian Metric Tensors to generate geometry-appropriate spacing and is capable of adaptive meshing from a spacing field generated either by the user or from solution data. FASTAR is a robust, general mesh generator that allows maximum flexibility with minimal post-processing

Using CFD in engine design

In this thesis the author presents two areas of work; exploring the integration of Computational Fluid Dynamics (CFD) into engine design for Jaguar Cars Ltd and developing a novel 'mesh construction' method for making mesh generation both easy and fast. It is concluded that Jaguar can use CFD in the evaluation stage of the engine design process, although not in the concept stage of design. The CFD predictions are shown to be useful for detecting flow related faults and determining the general flow trends, but they should not be used as an absolute measure of the flow variables. The author has determined an efficient method for obtaining good quality meshes using commercial modelling and mesh generation software which requires a skilled CFD analyst. Steady flow analysis of an engine port and cylinder design could currently be completed in about six weeks using a high-powered workstation. The author recommends dedicated workstations for CFD analysis and training Jaguar's draughtsmen to create CAD models with computer analysis requirements in mind. The author's mesh construction program automatically joins two overlapping meshes or cuts one mesh from another. Whilst the program works well on the test cases considered, it is not at a stage for commercial exploitation. Further development is therefore recommended

An adaptive hybrid mesh generation method for complex geometries

An adaptive hybrid mesh generation method is described to automatically provide spatial discretizations suitable for computational fluid dynamics or other 2D solver applications. This method employs a hierarchical grid generation technique to create a background mesh, an extrusion-type method for inserting boundary layers, and an unstructured triangulation to stitch between the boundary layers and background mesh. This method provides appropriate mesh resolution based on geometry segments from a file, and has the capability of adapting the background mesh based on a spacing field generated from solution data or some other arbitrary source. By combining multiple approaches to the grid generation process, this method seeks to benefit from the strengths of each, while avoiding the weaknesses of each. Possible future work to increase the robustness of the method is also discussed

On Tetrahedralisations Containing Knotted and Linked Line Segments

This paper considers a set of twisted line segments in 3d such that they form a knot (a closed curve) or a link of two closed curves. Such line segments appear on the boundary of a family of 3d indecomposable polyhedra (like the Schönhardt polyhedron) whose interior cannot be tetrahedralised without additional vertices added. On the other hand, a 3d (non-convex) polyhedron whose boundary contains such line segments may still be decomposable as long as the twist is not too large. It is therefore interesting to consider the question: when there exists a tetrahedralisation contains a given set of knotted or linked line segments? In this paper, we studied a simplified question with the assumption that all vertices of the line segments are in convex position. It is straightforward to show that no tetrahedralisation of 6 vertices (the three-line-segments case) can contain a trefoil knot. Things become interesting when the number of line segments increases. Since it is necessary to create new interior edges to form a tetrahedralisation. We provided a detailed analysis for the case of a set of 4 line segments. This leads to a crucial condition on the orientation of pairs of new interior edges which determines whether this set is decomposable or not. We then prove a new theorem about the decomposability for a set of n (n ≥ 3) knotted or linked line segments. This theorem implies that the family of polyhedra generalised from the Schonhardt polyhedron by Rambau [1] are all indecomposable