Interactive numerical flow visualization using stream surfaces

Abstract

Interactive Numerical Flow Visualization Using Stream Surfaces(Under the direction of Frederick P. Brooks, Jr.)Three-dimensional steady fluid flows are often numerically simulated over multiple overlapping curvilinear arrays of sample points. Such flows are often visualized using tangent curves or streamlines computed through the interpolated velocity field.A stream surface is the locus of an infinite number of streamlines rooted at all points along a short line segment or rake. Stream surfaces can depict the structure of a flow field more effectively than is possible with mere streamline curves, but careful placement of the rakes is needed to most effectively depict the important features of the flow. I have built visualization software which supports the interactive calculation and display of stream surfaces in flow fields represented on composite curvilinear grids. This software exploits several novel methods to improve the speed with which a particle may be advected through a vector field. This is combined with a new algorithm which constructs adaptively sampled polygonal models of stream surfaces.These new methods make stream surfaces a viable tool for interactive numerical flow visualization. Software based ori these methods has been used by scientists at the 1.1.3Numerical Flow Visualization . . 185 Table 3.1 Relative performance of four differencing methods. 75 Table 3.2 Performance of mixed-spaced streamline computation .. 89 LIST OF TABLES COMPUTATIONAL FLUID DYNAMICSThe study of fluid flow is typically comprised of three phases: the construction of a grid of node points, the calculation of the flow field sample values at these points, and the post-process visualization of the resulting data. The requirements of the first two tasks motivate the use of unusual data structures, which pose difficulty for the interactive visualization of the results. Grid GenerationThe flow simulation effort begins with a description of the surface of an object, usually by a sequence of digitized cross-sections or a collection of surface spline patches. The object may be as simple as a sphere or as intricate as the Space ShuttleOrbiter with solid rocket boosters, external fuel tank, and interconnection hardware [Pearce et al. 1993]. Some volume surrounding the object is then tessellated into cells. These cells are small enough that the flow field may be expected to vary only slightly through each one. The partial differential equations which govern fluid flow are then discretized and numerically solved over the collection of points which are the vertices of these cells.In Finite Element Analysis, the cells of an unstructured computational grid may have a variety of shapes and each node point may be shared by any number of cells. These general cells can be easily positioned around intricate domain boundaries, but this generality requires increased bookkeeping during the simulation follow the curved contours of the vehicle surface. As a result, the six faces of each cell are not planar, but are instead...

Lagrangian representations of flow fields with parameter curves

“…Since the seminal work of Hulquist [16], it has been the primary technique for calculating the trajectory of a particle in a flow field. In state-of-the-art flow visualization, the large majority of techniques utilize advection [19,20,27,21,24,3].…”

Easy integral surfaces

“…If triangles are used [Hul90, Hul92, GTS * 04] then an optimal tiling strategy should be included in order to prevent long, thin triangles. The approach of Hultquist [Hul90,Hul92] requires three data structures, two tracer structures and a ribbon structure. The two tracer structures are used to generate the sequence of points that define two flow lines S 0 and S 1 .…”

“…In contrast, the approach of Hultquist [Hul90,Hul92] requires new tracer and ribbon structures to be stored in the linked list which represents the front. Also previous methods describe how new particles are inserted in order to handle convergence (and divergence) but not when.…”

“…The result is a quad merging ( Figure 5). Hultquist's algorithm [Hul90,Hul92] requires the insertion of three new triangles which make the transition between the leading edges of two ribbons and the single leading edge of a new replacement. We point out that, once again, quad meshes result in a simpler mesh, see Figure 6.…”

“…A video demonstration of animated timelines and timeribbons created by our application is provided [MLZ]. Timelines and timeribbons would be possible to incorporate into previous algorithms [GTS * 04, Hul90,Hul92]. A surface parameterization, S ∈ [0, 1], t ∈ [0, Tmax], is required whereas timelines and timeribbons are a natural byproduct of our approach.…”