Keywords: computational steering, flow visualization, time-dependent vector fields, Lagrangian coherent structures, finite-time Lyapunov exponent, vector field topology, GPU.

However, since the vector field topology is strictly applicable and interpretable only for stationary vector fields, the concept of Lagrangian coherent structures present as ridges in the finite-time Lyapunov exponent (FTLE) is built upon. This allows to perform steering with respect to the true time-dependent dynamics in a given time scope. However, to unleash the full potential of computational steering, its application demands interactive performance to provide the engineer with instant feedback for control. FTLE is computed from independent trajectories inside a time interval, making it a computationally expensive procedure but well suited for parallelization.

In this paper, an exemplary steering system that performs simulation, FTLE computation, and visualization on graphics processing units (GPUs) in real-time is presented. In the performance-oriented system, the fluid is modelled with the incompressible Euler equations in two dimensions on a uniform grid and the methods and implementation details of the CUDA-based solver are described. The main contribution is the visualization of coherent structures with FTLE for interactive steering by manipulating boundary conditions, based on the insights from the visualization. Therefore, theoretical background about FTLE is presented and furthermore the practical meaning of coherent structures is discussed. It is shown how the computation of FTLE is implemented efficiently, which is crucial for responsive interaction. Together with standard flow visualization techniques like path lines or particle tracers, an engineer can steer the flow by manipulating boundary conditions such as solid obstacles or velocity profiles. The prototype supports a simple user interface for image-based editing of boundary conditions with instant feedback.

For evaluation, performance results are presented to demonstrate that the approach is capable of interactive steering on a single GPU. In addition, examples of typical applications for flow steering like air conditioning or airfoil design are shown.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £85 +P&P)