A data assimilation model for turbulent flows using continuous adjoint formulation

A generalized data assimilation model for turbulent flows using the continuous adjoint formulation is proposed. Within this formulation, the Spalart-Allmaras turbulence model is modified by adding a correction function beta as a spatially varying coefficient to the turbulence production term. The model-form error is thus corrected by optimizing the beta distribution, using the adjoint equations and the corresponding boundary conditions, to minimize the discrepancy between the predictions and observations. In addition, a constraint is applied to drive beta toward a large value to avoid the flow unsteadiness owing to the low eddy viscosity. The present adjoint-based data assimilation (ABDA) model is expected to be applicable to various flow conditions unsolvable by the simple optimization of the model constant. This model is fully equation-driven and is thus computationally cheaper than the discretized adjoint method, as well as convenient to be implemented in the existing computational fluid dynamics codes. The flow over a cylinder with synthetic observations, the free round jet, the flow over a hump, and the three-dimensional flow over a wall-mounted cube, all of which are challenging for original Reynolds-averaged Navier-Stokes simulations, are employed to successfully demonstrate the reliability and capacity of the present ABDA model. The first-order scheme applied to the adjoint equations exhibits little effects on the final assimilation results, but improves the robustness significantly, and drives beta to another solution that can also minimize the cost function. The present ABDA model is efficient in the heavy assimilation work of different types of shear and separated flows. Published by AIP Publishing.