A high-order spectral solver for dye evolution and particle residence time calculations

Numerical simulation of dyes and non-discrete particle residence time (PRT) calculations, governed by advection-diffusion partial differential equations (PDEs), are useful a posteriori analysis approaches for both experimental and computational fluid dynamics studies. This contribution presents a new Fourier continuation (FC-)based, high-order numerical methodology for solving such systems without numerical diffusion (or "pollution") errors. The efficacy of FC has already been demonstrated for many strictly hyperbolic PDEs, namely heterogeneous elastic and fluid-structure problems. Velocity data for the corresponding governing equations are produced by an in-house fluid-structure simulator based on a lattice Boltzmann method coupled to a Lagrangian-coordinate elasticity solver. The proposed approach can also be applied to velocity data collected through experimental techniques such as from particle image velocimetry. Convergence and error analyses are performed with both analytical and manufactured solutions. Realistic case studies in fluid dynamics and hemodynamics are presented to demonstrate the applicability of the proposed FC-based dye simulator.