We study three-dimensional isogeometric analysis (IGA) and the solution of the resulting system of linear equations via a direct solver. IGA uses highly continuous $C^{p-1}$Cp-1 basis functions, which provide multiple benefits in terms of stability and convergence properties. However, smooth basis significantly deteriorate the direct solver performance and its parallel scalability. As a partial remedy for this, refined Isogeometric Analysis (rIGA) method improves the sequential execution of direct solvers. The refinement strategy enriches traditional highly-continuous $C^{p-1}$Cp-1 IGA spaces by introducing low-continuity $C^0$C0-hyperplanes along the boundaries of certain pre-defined macro-elements. In this work, we propose a solution strategy for rIGA for parallel distributed memory machines and compare the computational costs of solving rIGA versus IGA discretizations. We verify our estimates with parallel numerical experiments. Results show that the weak parallel scalability of the direct solver improves approximately by a factor of $p^2$p2 when considering rIGA discretizations rather than highly-continuous IGA spaces.

A stand-alone visualization application has been developed by a multi-disciplinary, collaborative team with the sole purpose of creating an interactive exploration environment allowing turbulent flow researchers to experiment and validate hypotheses using visualization. This system has specific optimizations made in data management, caching computations, and visualization allowing for the interactive exploration of datasets on the order of 1TB in size. Using this application, the user (co-author Calo) is able to interactively visualize and analyze all regions of a transitional flow volume, including the laminar, transitional and fully turbulent regions. The underlying goal of the visualizations produced from these transitional flow simulations is to localize turbulent spots in the laminar region of the boundary layer, determine under which conditions they form, and follow their evolution. The initiation of turbulent spots, which ultimately lead to full turbulence, was located via a proposed feature detection condition and verified by experimental results. The conditions under which these turbulent spots form and coalesce are validated and presented.

Introduction The images shown in Figure 1 display a single time step of a turbulent flow simulation computed by Dr. Thomas J. R. Hughes, Professor of Aerospace Engineering, and Victor Calo at The University of Texas at Austin. This research examines how a fluid running over a flat plate suddenly becomes turbulent. The smooth flow seen at the left-hand side of the volume has low-amplitude fluctuations that interact with the smooth, laminar boundary layer of the fluid. As the energy of the fluctuations is convected downward into the boundary layer, there is a sudden explosion of the entire flow into turbulence. The left-most image of Figure 1 displays the left to right nature of the fluid as it passes over the flat plate, showing the turbulent boundary layer. The middle image shows the volumetric flow with sheet of particles inserted at designated locations to show increasing turbulent behavior. The right-most image in Figure 1 is a close up of particle sheets showing local velocity fluctuations inside the turbulent boundary layer.