1. Center for Process Simulation and Design, University of Illinois Robert B. Haber, Duane D. Johnson, Jonathan A. Dantzig, DMR Visualizing Shocks in Spacetime Finite Element Solutions Yuan Zhou and Michael Garland, University of Illinois Department of Computer Science
Objective: Shock waves drive many forms of material failure and transformation. Finding and visualizing shocks can provide significant insight into the structure of solutions as well as indicate likely areas of numerical error.
Approach: We quantify shock “strength” throughout spacetime using a gradient-based metric. Tying strength to opacity allows us to render shock surfaces that show the sweep of shocks over spacetime. Our method is scalable, with running time linear in the size of the solution and space requirements that depend only on the output resolution.
Impact: This work provides a powerful tool for visualizing shock wave propagation in 3-D spacetime domains. Beyond the elastodynamic problems on which we currently focus, it should prove valuable in a number of other domains such as fluid dynamics, earthquake simulation, seismic petroleum exploration and nondestructive methods for detecting internal flaws in metal castings and weldments.
Left: Spacetime finite element mesh for elastodynamic simulation of crack-tip wave scattering within an elastic solid subjected to shock loading. The propagation of shock waves is readily apparent from the pattern of mesh refinement.
Below: Two views of the spacetime shock-trajectory surfaces present in the solution. Each surface is pseudo-colored according to local shock strength.