A fully-differentiable compressible high-order computational fluid dynamics solver

• URL: http://arxiv.org/abs/2112.04979v1
• Date: Thu, 9 Dec 2021 15:18:51 GMT
• Title: A fully-differentiable compressible high-order computational fluid dynamics solver
• Authors: Deniz A. Bezgin, Aaron B. Buhendwa, Nikolaus A. Adams
• Abstract summary: compressible Navier-Stokes equations govern compressible flows and allow for complex phenomena like turbulence and shocks. Despite tremendous progress in hardware and software, the smallest length-scales in fluid flows still introduces prohibitive computational cost for real-life applications. We present a fully-differentiable three-dimensional framework for the computation of compressible fluid flows using high-order state-of-the-art numerical methods.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes equations govern compressible flows and allow for complex phenomena like turbulence and shocks. Despite tremendous progress in hardware and software, capturing the smallest length-scales in fluid flows still introduces prohibitive computational cost for real-life applications. We are currently witnessing a paradigm shift towards machine learning supported design of numerical schemes as a means to tackle aforementioned problem. While prior work has explored differentiable algorithms for one- or two-dimensional incompressible fluid flows, we present a fully-differentiable three-dimensional framework for the computation of compressible fluid flows using high-order state-of-the-art numerical methods. Firstly, we demonstrate the efficiency of our solver by computing classical two- and three-dimensional test cases, including strong shocks and transition to turbulence. Secondly, and more importantly, our framework allows for end-to-end optimization to improve existing numerical schemes inside computational fluid dynamics algorithms. In particular, we are using neural networks to substitute a conventional numerical flux function.

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