A mass conservative Kalman filter algorithm for thermo-computational fluid dynamics

Computational fluid-dynamics (CFD) is of wide relevance in engineering
and science, due to its capability of simulating the three-dimensional flow
at various scales. However, the suitability of a given model depends on the
actual scenarios which are encountered in practice. This challenge of model
suitability and calibration could be overcome by a dynamic integration of
measured data into the simulation. This paradigm is known as data-driven
assimilation (DDA). In this paper, the study is devoted to Kalman filtering,
a Bayesian approach, applied to Reynolds-Averaged Navier-Stokes (RANS)
equations for turbulent flow. The integration of the Kalman estimator into
the PISO segregated scheme was recently investigated by (1). In this work,
this approach is extended to the PIMPLE segregated method and to the ther-
modynamic analysis of turbulent flow, with the addition of a sub-stepping
procedure that ensures mass conservation at each time step and the com-
patibility among the unknowns involved. The accuracy of the algorithm is
verified with respect to the heated lid-driven cavity benchmark, incorporat-
ing also temperature observations, comparing the augmented prediction of
the Kalman filter with the CFD solution obtained on a very fine grid.