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A method for post-processing the velocity after a pressure projection is developed that helps to maintain stability in an under-resolved, inviscid, discontinuous element-based simulation for use in environmental fluid mechanics process studies. The post-processing method is needed because of spurious divergence growth at element interfaces due to the discontinuous nature of the discretization used. This spurious divergence eventually leads to a numerical instability. Previous work has shown that a discontinuous element-local projection onto the space of divergence-free basis functions is capable of stabilizing the projection method, but the discontinuity inherent in this technique may lead to instability in under-resolved simulations. By enforcing inter-element discontinuity and requiring a divergence-free result in the weak sense only, a new post-processing technique is developed that simultaneously improves smoothness and reduces divergence in the pressure-projected velocity field at the same time. When compared against a non-post-processed velocity field, the post-processed velocity field remains stable far longer and exhibits better smoothness and conservation properties.

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We apply a pseudospectral method to numerically study the dynamics of vortices found within a low viscosity non-Newtonian fluid with a Carreau fluid rheology. The application of a Carreau fluid rheology avoids the commonly observed complications in power-law models at zero strain-rate. We find that fluids with a shear thinning rheology will preserve the small scale features of the flow. In particular, for vortex-solid wall interactions, shear thinning fluids can exhibit behavior associated with Newtonian fluids at a much higher Reynolds number. This can include secondary vorticity generation, and multiple vortex-bottom collisions each marked by periods of higher bottom shear rates. Using a variety of experimentally determined parameters from the literature, we argue that these results have direct application to many non-Newtonian fluids, including non-Newtonian fluid mud layers found on lake and ocean bottoms.