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Lagrangian methods for modeling transport, mixing, and geochemical reactions
Schmidt, Michael J.
Schmidt, Michael J.
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2019
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This dissertation is concerned with methods for enhancing the current capabilities of Lagrangian (particle-tracking) methods for modeling transport, mixing, and geochemical reactions. We address the problem of fixed minimum particle numbers (previously dictated only by initial concentration statistics) by developing a method that employs Gaussian spatial kernels to reduce the required number of particles without introducing excess error. We demonstrate that the recently developed mass-transfer particle-tracking (MTPT) algorithm solves the diffusion equation with O(∆t) accuracy and can be used in conjunction with random walks to jointly simulate the distinct process of mixing and spreading. We extend the MTPT method to enable it to simulate chemical reactions involving aqueous and solid species via mobile and immobile particle interactions. We show that this mobile-immobile reactive particle-tracking (miRPT) algorithm can simulate an arbitrarily small amount of diffusion, and we apply it, with favorable results, to a calcite-dolomite reactive transport system that includes dissolution and precipitation reactions. We establish the numerical equivalence, under certain conditions, between smoothed-particle hydrodynamics (SPH) and MTPT methods, and we thus unify methods that were previously treated as distinct. As a result, these particle-tracking methods inherit a large body of theoretical underpinning. Finally, we apply the miRPT algorithm to a chemically-complex system involving the cycling of heavy metals in lake sediments, and we consider the effects of perturbing the spatial representation of solid species using immobile particles. In this analysis, we see that irregular distributions of solid species leads to increased variability in model results, and we see that this effect is greatest in areas where reactants are not in chemical equilibrium.
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