Dye experimentation is a widely used method in experimental fluid mechanics for flow analysis or for the study of the transport of particles within a fluid. This technique is particularly useful in biomedical diagnostic applications ranging from hemodynamic analysis of cardiovascular systems to ocular circulation. However, simulating dyes governed by convection-diffusion partial differential equations (PDEs) can also be a useful post-processing analysis approach for computational fluid dynamics (CFD) applications. Such simulations can be used to identify the relative significance of different spatial subregions in particular time intervals of interest in an unsteady flow field. Additionally, dye evolution is closely related to non-discrete particle residence time (PRT) calculations that are governed by similar PDEs. This contribution introduces a pseudo-spectral method based on Fourier continuation (FC) for conducting dye simulations and non-discrete particle residence time calculations without numerical diffusion errors. Convergence and error analyses are performed with both manufactured and analytical solutions. The methodology is applied to three distinct physical/physiological cases: 1) flow over a two-dimensional (2D) cavity; 2) pulsatile flow in a simplified partially-grafted aortic dissection model; and 3) non-Newtonian blood flow in a Fontan graft. Although velocity data is provided in this work by numerical simulation, the proposed approach can also be applied to velocity data collected through experimental techniques such as from particle image velocimetry.

翻译：染料实验是实验流体力学中用于流动分析或研究流体中粒子传输的常用方法。该技术尤其在生物医学诊断应用中具有重要价值，涵盖从心血管系统血流动力学分析到眼部循环等领域。然而，求解对流扩散偏微分方程（PDEs）对染料进行模拟，也可作为计算流体力学（CFD）应用中的一种有效后处理分析方法。此类模拟可用于识别非定常流场中特定时空子区域在感兴趣时间区间内的相对重要性。此外，染料演化与受相似偏微分方程支配的非离散粒子停留时间（PRT）计算密切相关。本文提出一种基于傅里叶延拓（FC）的伪谱方法，用于实现无数值扩散误差的染料模拟与非离散粒子停留时间计算。通过人工解与解析解进行了收敛性与误差分析。该方法被应用于三个不同的物理/生理学案例：1）二维（2D）腔体上方流动；2）简化部分覆膜主动脉夹层模型中的脉动流动；3）Fontan移植血管中的非牛顿血流。尽管本文通过数值模拟获取速度数据，但所提方法同样适用于通过实验技术（如粒子图像测速法）采集的速度数据。