Tom Bobach

Surface techniques for vortex visualization

This paper presents powerful surface based techniques for the analysis of complex flow fields resulting from CFD simulations. Emphasis is put on the examination of vortical structures. An improved method for stream surface computation that delivers accurate results in regions of intricate flow is presented, along with a novel method to determine boundary surfaces of vortex cores. A number of surface techniques are presented that aid in understanding the flow behavior displayed by these surfaces. Furthermore, a scheme for phenomenological extraction of vortex core lines using stream surfaces is discussed and its accuracy is compared to one of the most established standard techniques.

Generation of Accurate Integral Surfaces in Time-Dependent Vector Fields

We present a novel approach for the direct computation of integral surfaces in time-dependent vector fields. As opposed to previous work, which we analyze in detail, our approach is based on a separation of integral surface computation into two stages: surface approximation and generation of a graphical representation. This allows us to overcome several limitations of existing techniques. We first describe an algorithm for surface integration that approximates a series of time lines using iterative refinement and computes a skeleton of the integral surface. In a second step, we generate a well-conditioned triangulation. Our approach allows a highly accurate treatment of very large time-varying vector fields in an efficient, streaming fashion. We examine the properties of the presented methods on several example datasets and perform a numerical study of its correctness and accuracy. Finally, we investigate some visualization aspects of integral surfaces.

A tetrahedra-based stream surface algorithm

This paper presents a new algorithm for the calculation of stream surfaces for tetrahedral grids. It propagates the surface through the tetrahedra, one at a time, calculating the intersections with the tetrahedral faces. The method allows us to incorporate topological information from the cells, e.g. critical points. The calculations are based on barycentric coordinates, since this simplifies the theory and the algorithm. The stream surfaces are ruled surfaces inside each cell, and their construction starts with line segments on the faces. Our method supports the analysis of velocity fields resulting from computational fluid dynamics (CFD) simulations.

Natural neighbor extrapolation using ghost points

Among locally supported scattered data schemes, natural neighbor interpolation has some unique features that makes it interesting for a range of applications. However, its restriction to the convex hull of the data sites is a limitation that has not yet been satisfyingly overcome. We use this setting to discuss some aspects of scattered data extrapolation in general, compare existing methods, and propose a framework for the extrapolation of natural neighbor interpolants on the basis of dynamic ghost points.

Accurate and Efficient Visualization of Flow Structures in a Delta Wing Simulation

The paper is concerned with the extraction and visualization of structural features in delta wing dataset resulting from a large-scale Reynolds Averaged Navier-Stokes simulation. Its main contributions are two novel schemes designed for this purpose. First, we introduce a new method for fast and precise extraction of separation and attachment lines on the body of the delta wing. Second, we improve signican tly standard stream surface computation schemes to achieve accurate integration even in regions exhibiting complex structures. Additional state-of-the-art o w visualization techniques are used to complete the study of the dataset. The main focus is on the interaction between open separation and attachment lines of the wall shear stress on one hand, and vortices that form in the vicinity of the delta wing on the other hand. These features are key factors in igh t stability and their study is mandatory in aircraft design. The paper demonstrates the power of a combined use of line-type feature extraction and stream surface computation to deeply improve understanding of three-dimensional structures and ease the analysis of o w separation and vortex breakdown.

Geometric properties of the adaptive delaunay tessellation

Recently, the Adaptive Delaunay Tessellation (Adt) was introduced in the context of computational mechanics as a tool to support Voronoi-based nodal integration schemes in the finite element method. While focusing on applications in mechanical engineering, the former presentation lacked rigorous proofs for the claimed geometric properties of the Adt necessary for the computation of the nodal integration scheme. This paper gives pending proofs for the three main claims which are uniqueness of the Adt, connectedness of the Adt, and coverage of the Voronoi tiles by adjacent Adt tiles. Furthermore, this paper provides a critical assessment of the Adt for arbitrary point sets.

Discrete harmonic functions from local coordinates

In this work we focus on approximations of continuous harmonic functions by discrete harmonic functions based on the discrete Laplacian in a triangulation of a point set. We show how the choice of edge weights based on generalized barycentric coordinates influences the approximation quality of discrete harmonic functions. Furthermore, we consider a varying point set to demonstrate that generalized barycentric coordinates based on natural neighbors admit discrete harmonic functions that continuously depend on the point set.

Issues and implementation of C 1 and C 2 natural neighbor interpolation

Smooth local coordinates have been proposed by Hiyoshi and Sugihara 2000 to improve the classical Sibsons and Laplace coordinates. These smooth local coordinates are computed by integrating geometric quantities over weights in the power diagram. In this paper we describe how to efficiently implement the Voronoi based C2 local coordinates. The globally C2 interpolant that Hiyoshi and Sugihara presented in 2004 is then compared to Sibsons and Farins C1 interpolants when applied to scattered data interpolation.