An UQ-ready finite element solver for a two-dimensional RANS model of free plane jets
This work addresses the need for differentiable RANS solvers for uncertainty quantification in computational fluid dynamics, but is incremental as it focuses on a specific 2D free plane jet case.
The authors developed a smoothly differentiable finite element solver for 2D RANS with k-ε turbulence model, enabling scalable Hessian-based uncertainty quantification. The solver provides forward, adjoint, and higher derivative capabilities without non-differentiable perturbations.
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.