Separation and attachment lines are topologically significant curves that exist on 2D surfaces in 3D vector fields. Two algorithms are presented, one point-based and one element-based, that extract separation and attachment lines using eigenvalue analysis of a locally linear function. Unlike prior techniques based on piecewise numerical integration, these algorithms use robust analytical tests that can be applied independently to any point in a vector field. The feature extraction is fully automatic and suited to the analysis of large-scale numerical simulations. The strengths and weaknesses of the two algorithms are evaluated using analytic vector fields and also results from computational fluid dynamics (CFD) simulations. We show that both algorithms detect open separation lines-a type of separation that is not captured by conventional vector field topology algorithms.

A recently completed implementation of a virtual environment for exploring numerically generated three-dimensional unsteady flowfields is described. A boom-mounted six-degree-of-freedom head-position-sensitive stereo CRT system is used for viewing. A hand-position-sensitive glove controller is used for injecting various tracers (e.g. smoke) into the virtual flowfield. A multiprocessor graphics workstation is used for computation and rendering. The techniques for visualizing unsteady flows are described, and the computer requirements for a variety of visualization techniques are discussed. These techniques generalize to visualization of other 3D vector fields.>

A description is given of a software system, TOPO, that numerically analyzes and graphically displays topological aspects of a three-dimensional vector field, v, to produce a single, relatively simple picture that characterizes v. The topology of v considered consists of its critical points (where v=0), their invariant manifolds, and the integral curves connecting these invariant manifolds. The field in the neighborhood of each critical point is approximated by the Taylor expansion. The coefficients of the first nonzero term of the Taylor expansion around a critical point are the 3*3 matrix Delta v. Critical points are classified by examining Delta v's eigenvalues. The eigenvectors of Delta v span the invariant manifolds of the linearized field around a critical point. Curves integrated from initial points on the eigenvectors a small distance from a critical point connect with other critical points (or the boundary) to complete the topology. One class of critical surfaces that is important in computational fluid dynamics is analyzed.>

A new method for the solution of pentadiagonal systems of linear equations is presented. The method is a generalization of ordinary odd-even elimination used for tridiagonal systems. Using n processors, an n X n pentadiagonal system can be solved using the new method (generalized odd-even elimination) in time proportional to log2 n.