Eric Liu

Over the past few decades, Computational Fluid Dynamics (CFD) models have become a critical part of most aircraft design efforts. Unfortunately the tools in use today are not sufficiently accurate; they cannot answer modern engineering questions with a reasonable level of confidence. For example, a recent AIAA survey of various CFD solvers found a 1e-3 variation in their drag coefficient predictions, a level of error which translates to the loss of as many as 100 passengers on a long range transport aircraft. Part of the issue is that many current codes were designed to run on 1990s supercomputers - computing power which is available in today's commodity clusters.

I plan to work on the development of new high fidelity CFD routines with increased levels of automation. In particular, I am interested in Finite Element Methods in a higher order, Discontinuous-Galerkin (DG) framework. Among other advantages, higher order methods allow for increased resolution of flow phenomena and faster solution convergence. One drawback of DG is that there is redundancy in the degrees of freedom since we allow discontinuities at element boundaries. Nonetheless, DG offers significant algorithmic advantages, increased stability, and high parallelizability, making the extra cost arguably worthwhile. Given the amount of computing power available to us, higher order DG methods are potentially one way of working toward more accurate CFD models.

One specific application that I will be pursuing is the accurate prediction of flow transition in hypersonic flow regimes. Due to the difficulty of running experiments in hypersonic flows, relatively little is known (experimentally) about this problem. Accurate computational methods are critical to future hypersonic aircraft designs since researchers have very few predictive tools available to them.

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