Physical interactions between a fluid and structure, potentially manifested as self-sustained or divergent oscillations, can be sensitive to many parameters whose values are uncertain. Of interest here are aircraft aeroelastic interactions, which must be accounted for in aircraft certification and design. Deterministic prediction of these aeroelastic behaviors can be difficult owing to physical and computational complexity. New challenges are introduced when physical parameters and elements of the modeling process are uncertain. By viewing aeroelasticity through a nondeterministic prism, where key quantities are assumed stochastic, one may gain insights into how to reduce system uncertainty, increase system robustness, and maintain aeroelastic safety. This article reviews uncertainty quantification in aeroelasticity using traditional analytical techniques not reliant on computational fluid dynamics; compares and contrasts this work with emerging methods based on computational fluid dynamics, which target richer physics; and reviews the state of the art in aeroelastic optimization under uncertainty. Barriers to continued progress, for example, the so-called curse of dimensionality, are discussed.

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Direct Simulation Monte Carlo (DSMC) methods for the Boltzmann equation employ a point measure approximation to the distribution function, as simulated particles may possess only a single velocity. This representation limits the method to converge only weakly to the solution of the Boltzmann equation. Utilizing kernel density estimation we have developed a stochastic Boltzmann solver which possesses strong convergence for bounded and L∞ solutions of the Boltzmann equation. This is facilitated by distributing the velocity of each simulated particle instead of using the point measure approximation inherent to DSMC. We propose that the development of a distributional method which incorporates distributed velocities in collision selection and modeling should improve convergence and potentially result in a substantial reduction of the variance in comparison to DSMC methods. Toward this end, we also report initial findings of modeling collisions distributionally using the Bhatnagar-Gross-Krook collision operator.