Publications

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Reynolds-Averaged Navier-Stokes models are not very accurate for high-Reynolds-number compressible jet-incrossflow interactions. The inaccuracy arises from the use of inappropriate model parameters and model-form errors in the Reynolds-Averaged Navier-Stokes model. In this work, the hypothesis is pursued that Reynolds-Averaged Navier-Stokes predictions can be significantly improved by using parameters inferred from experimental measurements of a supersonic jet interacting with a transonic crossflow.ABayesian inverse problem is formulated to estimate three Reynolds-Averaged Navier-Stokes parameters (Cμ;Cϵ2;Cϵ1), and a Markov chain Monte Carlo method is used to develop a probability density function for them. The cost of the Markov chain Monte Carlo is addressed by developing statistical surrogates for the Reynolds-Averaged Navier-Stokes model. It is found that only a subset of the (Cμ;Cϵ2;Cϵ1) spaceRsupports realistic flow simulations.Ris used as a prior belief when formulating the inverse problem. It is enforced with a classifier in the current Markov chain Monte Carlo solution. It is found that the calibrated parameters improve predictions of the entire flowfield substantially when compared to the nominal/ literature values of (Cμ;Cϵ2;Cϵ1); furthermore, this improvement is seen to hold for interactions at other Mach numbers and jet strengths for which the experimental data are available to provide a comparison. The residual error is quantifies, which is an approximation of the model-form error; it is most easily measured in terms of turbulent stresses.

We present a general technique to solve Partial Differential Equations, called robust stencils, which make them tolerant to soft faults, i.e. bit flips arising in memory or CPU calculations. We show how it can be applied to a two-dimensional Lax-Wendroff solver. The resulting 2D robust stencils are derived using an orthogonal application of their 1D counterparts. Combinations of 3 to 5 base stencils can then be created. We describe how these are then implemented in a parallel advection solver. Various robust stencil combinations are explored, representing tradeoff between performance and robustness. The results indicate that the 3-stencil robust combinations are slightly faster on large parallel workloads than Triple Modular Redundancy (TMR). They also have one third of the memory footprint. We expect the improvement to be significant if suitable optimizations are performed. Because faults are avoided each time new points are computed, the proposed stencils are also comparably robust to faults as TMR for a large range of error rates. The technique can be generalized to 3D (or higher dimensions) with similar benefits.

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Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of a system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation.We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equations at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. The goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.

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Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) and fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO2 (ffCO2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO2 emissions and synthetic observations of ffCO2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.