Reduced-order models (ROMs) are commonly used to reduce the complexity of large-scale fluid dynamics problems. The main technique to obtain their basis is proper orthogonal decomposition (POD), where an energy-based basis is obtained. Such a basis is derived without considering the governing equations. Moreover, if the flow dynamics are not energy-dominated, the resulting POD-ROM can be biased towards that quantity and not represent the case properly.

In this project, a constrained goal-oriented reduced-order modeling (GOROM) technique that optimizes the modes of POD-ROMs is applied to wall-bounded flows. Its semi-continuous formulation allows great flexibility in treating non-linear problems with discrete reference datasets and complex goal functionals, and since the model constraint is considered in the optimization, the output model has a more complete physical interpretation.

Two cases are considered. First, a 1D Burgers equation forced with data from a turbulent channel flow is studied. Different ROM sizes and goal functionals are tested and compared to the reference data statistics. After that, a 3D transitional channel is studied, with a reference dataset that is generated using an initial condition that experiences transient growth. In this case, the ROM size is fixed and the goal functionals used are related to this phenomenon.

The results for the Burgers case show the superiority of the GOROM compared to a POD-ROM. They also depend on the initial guess for the optimization modes, and it is shown how the choice of the goal functional influences the behavior of the solution. After that, the transitional channel highlights the influence of truncation on transient growth problems and shows the model constraint improves the growth prediction significantly. Finally, the use of dedicated goal functionals is shown to improve the prediction of relevant quantities such as the production of kinetic energy.