## Identifier

etd-06112014-141645

## Degree

Doctor of Philosophy (PhD)

## Department

Computer Science

## Document Type

Dissertation

## Abstract

The complexity of large scale computational fluid dynamic simulations (CFD) demands powerful tools to investigate the numerical results. To analyze and understand these voluminous results, we need to visualize the 3D flow field. We chose to use a visualization technique called Time Surfaces. A time surface is a set of surfaces swept by an initial seed surface for a given number of timesteps. We use a front tracking approach where the points of an in initial surface are advanced in a Lagrangian fashion. To maintain a smooth time surface, our method requires surface refinement operations that either split triangle edges, adjust narrow triangles, or delete small triangles. In the conventional approach of edge splitting, we compute the length of an edge, and split that edge if it has exceeded a certain threshold length. In our new approach, we examine the angle between the two vectors at a given edge. We split the edge if the vectors are diverging from one another. This vector angle criterion enables us to refine an edge before advancing the surface front. Refining a surface prior to advancing it has the effect of minimizing the amount of interpolation error. In addition, unlike the edge length criterion which yields a triangular mesh with even vertex distribution throughout the surface, the vector angle criterion yields a triangular mesh that has fewer vertices where the vector field is flat and more vertices where the vector field is curved. Motivated by the evaluation and the analysis of flow field mixing quantities, this work explores two types of quantitative measurements. First, we look at Ottino's mixing indicators which measure the degree of mixing of a fluid by quantifying the rate at which a sample fluid blob stretches in a flow field over a period of time. Using the geometry of the time surfaces we generated, we are able to easily evaluate otherwise complicated mixing quantities. Second, we compute the curvature and torsion of the velocity field itself. Visualizing the distribution and intensity of the curvature and torsion scalar fields enables us to identify regions of strong and low mixing. To better observe these scalar fields, we designed a multi-scale colormap that emphasizes small, medium, and large values, simultaneously. We test our time surface method and analyze fluid flow mixing quantities on two CFD datasets: a stirred tank simulation and a BP oil spill simulation.

## Date

2014

## Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

## Recommended Citation

Harhad, Farid, "Evolving time surfaces and tracking mixing indicators for flow visualization" (2014). *LSU Doctoral Dissertations*. 1603.

https://repository.lsu.edu/gradschool_dissertations/1603

## Committee Chair

Karki, Bijaya

## DOI

10.31390/gradschool_dissertations.1603