An arbitrarily high-order, non-dissipative, and kinetic-energy conserving HDG numerical method to simulate incompressible flows in complex geometries and its application to PTV data assimilation

Non-dissipativity and kinetic energy conservation are two essential features of the base numerical method for a reliable and stable large-eddy simulation. Such numerical methods for incompressible flow simulation in complex geometries have been, at maximum, second-order accurate, until now. In this talk, we will, for the first time, present such a numerical method that is arbitrarily high-order accurate. This method is built using the Hybridized Discontinuous Galerkin (HDG) framework. It uses a simplicial mesh and is hence applicable to a real-world complex geometry. The details of the method and numerical experiments demonstrating its unique features will be presented and its broader implications will be discussed. We will also present a data assimilation application of the high-order method to reconstruct volumetric quantities from Particle Tracking Velocimetry (PTV) measurements. Using this assimilation strategy, a high-order approximation to the velocity gradient tensor and pressure can be obtained from the PTV measurements. The accuracy of the reconstructed quantities will be investigated for a few different flows.