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Numerical solution of the system of partial differential equations arisingfrom the Reynolds-Averaged Navier-Stokes (RANS) equations with $k-\epsilon$turbulence model presents several challenges due to the advection dominatednature of the problem and the presence of highly nonlinear reaction terms.State-of-the-art software for the numerical solution of the RANS equationsaddress these challenges by introducing non-differentiable perturbations in themodel to ensure numerical stability. However, this approach leads todifficulties 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 solvercapabilities but also adjoint and higher derivatives capabilities.

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