Numerical Investigation of Richtmyer-Meshkov Instability in Reactive Gas Mixtures
Final Report Abstract
The original project objectives were the quantification of uncertainties in mixing and reaction of the reactive shock-bubble interaction due to the propagation of initial-data and parameter uncertainties, and the extension of the two-dimensional direct numerical simulation (DNS) to three dimensions. The latter objective has been partially achieved by extending the available 2D reactive-shock-bubble-interaction (RSBI) DNS framework INCA. Only one of the initially planned three different 3D cases has been investigated eventually. Different chemical reaction mechanisms for the hydrogen-oxygen mixture have been scrutinized with respect to the best compromise between computational efficiency and accuracy, analyzed for their sensitivities. Out of the 4 analyzed reaction mechanisms the Ó Conaire mechanism was found to be the most effective. The first objective parameter studies revealed that the original plan of employing INCA within the non-intrusive uncertainty-quantification toolkit DAKOTA would result in inacceptable computational cost, despite favorable experiences for non-reactive shock-bubble interactions, due to the enhanced parameter space and more complex stochastic behavior in the reacting case requiring significantly more simulations for statistically converged results. It was decided to deviate from the original plan and to re-engineer the entire uncertainty-quantification (UQ) workflow. Instead of polynomial chaos approaches, as provided by DAKOTA, we decided to follow a multi-fidelity Bayesian approach based on multi-fidelity Monte-Carlo sampling and variance reduction. Multi-fidelity exploits the correlation-structure between mesh-resolutions, and reaction-model complexities to reduce the computational cost of the statistical inference. The workflow has been implemented using the scheduling framework MERLIN. However, beyond initial functionality tests, full-setup runs involving HPC installations at HLRS and JSC were not yet possible to us due to limited hardware availability and stability. We identified an alternative approach based on the automated workflow system AiiDA but have not been able to fully implement the workflow and test it yet. From the incomplete work on the first objective, we conclude that principal approaches on how to deal with data-intensive machine-learning workflows in fluid mechanics have been established, but a gap between software-stack, its realization using on-premise hardware, and workflow orchestration still exists and requires closer integration between simulation groups and HPC centers. As key enabler towards affordable Bayesian multifidelity UQ, the ability to generate gradients along DNS trajectories has been identified. Automatic differentiation (AD) has been identified as the most suitable approach as classical adjoint-based approaches are far too costly to be computationally tractable. A major part of the research work has been devoted to establish a compiler-based AD capability based on the recently developed ENZYME plugin. In cooperation with the developer team of the framework, the capabilities of ENZYME to deal with different parallelization paradigms and to run on GPU accelerators have been developed, verified, and incorporated into ENZYME. Moreover, INCA code has been re-written to enable automatic differentiation. As a side project along with the different coding and implementation tasks, we have revisited the question of generating modified differential equations for generic numerical schemes by learning from data. The modified equation delivers information of the effective physical model represented by the numerical scheme, which is particularly relevant whenever the truncation error is not asymptotically small, as in typical simulation applications of the current project. Analytical derivation of the modified equation for more complex discretization scheme is difficult. We have established a data-driven sparse identification of truncation errors (SITE) which returns the leading-order terms of the modified equation from a symbolic regression library.
Publications
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2019. Sparse identification of truncation errors. Journal of Computational Physics, 397, p.108851
Thaler, S., Paehler, L. and Adams, N.A.
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2021, November. Reverse-mode automatic differentiation and optimization of GPU kernels via enzyme. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (pp. 1-16)
Moses, W.S., Churavy, V., Paehler, L., Hückelheim, J., Narayanan, S.H.K., Schanen, M. and Doerfert, J.
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2022, November. Scalable Automatic Differentiation of Multiple Parallel Paradigms through Compiler Augmentation. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (pp. 859-876). ISBN: 978-1-6654-5444-5
Moses, W.S., Narayanan, S.H.K., Paehler, L., Churavy, V., Schanen, M., Hückelheim, J., Doerfert, J. and Hovland, P.
