Accurate computational representations of highly deformable surfaces are indispensable in the fields of computer animation, medical simulation, computer vision, digital modeling, and computational physics. The focus of this dissertation is on the animation of physics-based phenomena with highly detailed deformable surfaces represented by triangle meshes. We first present results from an algorithm that generates continuum mechanics animations with intricate surface features. This method combines a finite element method with a tetrahedral mesh generator and a high resolution surface mesh, and it is orders of magnitude more efficient than previous approaches. Next, we present an efficient solution for the challenging problem of computing topological changes in detailed dynamic surface meshes. We then introduce a new physics-inspired surface tracking algorithm that is capable of preserving arbitrarily thin features and reproducing realistic fine-scale topological changes like Rayleigh-Plateau instabilities. This physics-inspired surface tracking technique also opens the door for a unique coupling between surficial finite element methods and volumetric finite difference methods, in order to simulate liquid surface tension phenomena more efficiently than any previous method. Due to its dramatic increase in computational resolution and efficiency, this method yielded the first computer simulations of a fully developed crown splash with droplet pinch off.

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Simulations were performed to evaluate solution adaptive meshing strategies for flows with vortices whose axes of rotation are parallel to the bulk fluid motion. Two configurations were investigated: a wing in a wind tunnel and a missile spinning at 30Hz and 60Hz at 0◦ angle of attack with canards deflected 15◦. Feature-based descriptors were used to identify regions of the flow near vortices that are candidate regions for adaptive meshing. Several different adaptive meshing techniques were evaluated. These techniques include refinement around the vortex core, refinement near the vortex extent surface, refinement inside the extent surface, refinement inside and near the extent surface, and mesh regeneration using the vortex extent surface as an embedded surface. Results for the wing case, compared to experimental data, indicate that it is necessary to refine the region within and near the vortex extent surface to accurately recreate physical characteristics and achieve an acceptable solution.

Shear layer development over a NACA 0018 airfoil at a chord Reynolds number of 100,000 was investigated experimentally. The effects of experimental setup and analysis tools on the results were also examined. The sensitivity of linear stability predictions for measured separated shear layer velocity profiles to both the analysis approach and experimental data scatter was evaluated. Analysis approaches that are relatively insensitive to experimental data scatter were identified. Stability predictions were shown to be more sensitive to the analysis approach than to experimental data scatter, with differences in the predicted maximum disturbance growth rate and corresponding frequency of approximately 35% between approaches. A parametric study on the effects of experimental setup on low Reynolds number airfoil experiments was completed. It was found that measured lift forces and vortex shedding frequencies were affected by the end plate configuration. It was concluded that the ratio of end plate spacing to projected model height should be at least seven, consistent with the guideline for circular cylinders. Measurements before and after test section wall streamlining revealed errors in lift coefficients due to blockage as high as 9% and errors in the wake vortex shedding frequency of 3.5%. Shear layer development over the model was investigated in detail. Flow visualization images linked an observed asymmetry in wake velocity profiles to pronounced vortex roll-up below the wake centerline. Linear stability predictions based on the mean hot-wire profiles were found to agree with measured disturbance growth rates, wave numbers, and streamwise velocity fluctuation profiles. Embedded surface pressure sensors were shown to provide reasonable estimates of disturbance growth rate, wave number, and convection speed for conditions at which a separation bubble formed on the airfoil surface. Convection speeds of between 30 and 50% of the edge velocity were measured, consistent with phase speed estimates from linear stability theory.

Shear layer development over a NACA 0018 airfoil at a chord Reynolds number of 100,000 was investigated experimentally. The effects of experimental setup and analysis tools on the results were also examined. The sensitivity of linear stability predictions for measured separated shear layer velocity profiles to both the analysis approach and experimental data scatter was evaluated. Analysis approaches that are relatively insensitive to experimental data scatter were identified. Stability predictions were shown to be more sensitive to the analysis approach than to experimental data scatter, with differences in the predicted maximum disturbance growth rate and corresponding frequency of approximately 35% between approaches. A parametric study on the effects of experimental setup on low Reynolds number airfoil experiments was completed. It was found that measured lift forces and vortex shedding frequencies were affected by the end plate configuration. It was concluded that the ratio of end plate spacing to projected model height should be at least seven, consistent with the guideline for circular cylinders. Measurements before and after test section wall streamlining revealed errors in lift coefficients due to blockage as high as 9% and errors in the wake vortex shedding frequency of 3.5%. Shear layer development over the model was investigated in detail. Flow visualization images linked an observed asymmetry in wake velocity profiles to pronounced vortex roll-up below the wake centerline. Linear stability predictions based on the mean hot-wire profiles were found to agree with measured disturbance growth rates, wave numbers, and streamwise velocity fluctuation profiles. Embedded surface pressure sensors were shown to provide reasonable estimates of disturbance growth rate, wave number, and convection speed for conditions at which a separation bubble formed on the airfoil surface. Convection speeds of between 30 and 50% of the edge velocity were measured, consistent with phase speed estimates from linear stability theory.