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Dye experimentation is a widely used method in experimental fluid mechanicsfor flow analysis or for the study of the transport of particles within afluid. This technique is particularly useful in biomedical diagnosticapplications ranging from hemodynamic analysis of cardiovascular systems toocular circulation. However, simulating dyes governed by convection-diffusionpartial differential equations (PDEs) can also be a useful post-processinganalysis approach for computational fluid dynamics (CFD) applications. Suchsimulations can be used to identify the relative significance of differentspatial subregions in particular time intervals of interest in an unsteady flowfield. Additionally, dye evolution is closely related to non-discrete particleresidence time (PRT) calculations that are governed by similar PDEs. Thiscontribution introduces a pseudo-spectral method based on Fourier continuation(FC) for conducting dye simulations and non-discrete particle residence timecalculations without numerical diffusion errors. Convergence and error analysesare performed with both manufactured and analytical solutions. The methodologyis applied to three distinct physical/physiological cases: 1) flow over atwo-dimensional (2D) cavity; 2) pulsatile flow in a simplifiedpartially-grafted aortic dissection model; and 3) non-Newtonian blood flow in aFontan graft. Although velocity data is provided in this work by numericalsimulation, the proposed approach can also be applied to velocity datacollected through experimental techniques such as from particle imagevelocimetry.

A Fourier-based methodology without numerical diffusion for conducting dye simulations and particle residence time calculations