Efficient reconstruction of flow field with pressure from particle tracks: VIC#

A data assimilation-based method, which supplements additional constraints and coarse-grid approximation to Vortex-in-Cell-plus (VIC+), is proposed. An instantaneous pressure field is optimized in addition to and simultaneously with vorticity, velocity and acceleration fields. Not only a disparity between measurement and reconstruction at each particle position but also grid-based residuals from the additional constraints are minimized by an iterative optimization procedure. The additional constraints are derived from the Navier-Stokes equation, continuity equations, and vector calculus identities. Larger flow structures are mainly reconstructed by the coarse-grid approximation which consists of multiple schemes with various grid sizes, and thus computation time is saved. The coarse-grid approximation also contributes to stable convergence because of refined initial guesses for finer-grid schemes and therefore leads to smaller residuals at the finest-grid scheme. Experimental 4D PTV data obtained by Shake-the-Box (STB) is dealt with by the present method, Vortex-in-Cell-sharp (VIC#), and its reconstructed fluid structure, pressure field, and computational performances are analyzed.