Eulerian time-marching in Vortex-In-Cell (VIC) method: reconstruction of multiple time-steps from a single vorticity volume and time-resolved boundary condition

A data assimilation approach is proposed to enhance the dynamic range of Vortex-In-Cell (VIC) method by simulating future- and past- instances. The VIC mainly considers a vorticity field from which velocity acceleration fields are calculated through Poisson equations, respectively bounded prescribed conditions. In addition, time derivative also available transport equation. focuses on such already data, i.e., its fields, for additional instances getting feedbacks corresponding measurement instances, e.g., particle image velocimetry (PTV). However, self-simulated flow can be depleted due lack incoming information, out reconstruction domain at source instance. To supply that kind information thus sustain simulation, boundary conditions simulated required considered. As result, gather corrections multiple PTV while optimizing single volume time-resolved Since grid points much smaller in number than whole volume, one expect an increased range. former work, VIC# (Jeon et al. 2018), supplements constraints coarse-grid approximation VIC+ (Schneiders Scarano 2016), selected as 3D 4D applied. Two explicit Eulerian time-marching methods tested simulation scheme: forward Euler Runge-Kutta methods. numerical assessment conducted using synthetic whose ground truth known, returns qualities based identified vortical structures. Other practical features regarding convergence computation complexity reported. visually verify improvement approach, two kinds Shake-the-Box (STB) measurements, were acquired high-speed systems, processed discussed.