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arXiv · 1712.01786

An UQ-ready finite element solver for a two-dimensional RANS model of free plane jets

Umberto Villa·Alexandre Noll Marques
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Abstract

Numerical solution of the system of partial differential equations arising from the Reynolds-Averaged Navier-Stokes (RANS) equations with $k-ε$ turbulence model presents several challenges due to the advection dominated nature of the problem and the presence of highly nonlinear reaction terms. State-of-the-art software for the numerical solution of the RANS equations address these challenges by introducing non-differentiable perturbations in the model to ensure numerical stability. However, this approach leads to difficulties in the formulation of the higher-order forward/adjoint problems, which are needed for scalable Hessian-based uncertainty quantification (UQ) methods. In this note, we present the construction of a UQ-ready flow solver, i.e., one that is smoothly differentiable and provides not only forward solver capabilities but also adjoint and higher derivatives capabilities.

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Umberto Villa, Alexandre Noll Marques. 2017-12-05. An UQ-ready finite element solver for a two-dimensional RANS model of free plane jets. https://arxiv.org/abs/1712.01786

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