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A novel state observer-based data-assimilation technique is described and then assessed with a numerical test case. This novel technique assimilates pressure data through a state observer that is constructed based on a proportional-integral-derivative control law and that acts on the pressure equation. The technique is assessed by comparing the performance to a standard simulation and a data-assimilated simulation using a previously-established technique, wherein a proportional observer is placed in the momentum equations. First, the mechanism through which measured pressure data is assimilated into simulations is described for both the previously-established and the novel technique. Next, the techniques are applied to a square cylinder in cross-flow at a Reynolds number of 100. A reference simulation is run on a dense mesh, and both standard and data-assimilated simulations are run on a much coarser mesh. The primary characteristic used to evaluate the techniques is their dynamic performance, in terms of how quickly vortex shedding is realized and how accurately the frequency of the vortex shedding is modeled on the coarser mesh. Both of the data assimilation techniques produce simulations with a much faster transition from initial conditions to vortex shedding than the standard simulation on the coarse mesh. The data-assimilated simulation using an observer in the pressure equations most accurately estimates the pressures and velocities at the probed locations and produces a frequency spectrum that most closely matches the reference simulation.

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