This report is split into two main topics. The first topic is focused on using high-order Gaussian Processes (GP) for the reconstruction of cell data in numerical simulations. We first present a generalization to previous work, allowing GP to predict any linear operator. This strategy has the potential to increase the efficiency of sophisticated numerical methods and provides a general framework for computing high-order estimates for any linear operator. We present convergence tables and plots for a set of smooth benchmark problems. We then study GP's behavior for the reconstruction of discontinuous data and find that high-order GPs suffer from oscillations near discontinuities, similar to their high-order polynomial counterparts. To address the oscillations in GPs, we introduce a new second-order kernel, Discontinous Arcsin (DAS), that is stationary and prevents oscillations. DAS is integrated into a shock-capturing framework called the Multidimensional Optimal Order Detection (MOOD) method. The MOOD method is an a-posteriori order cascading method that drops the order of reconstruction at shocks for stability. In a three-order cascade scenario (e.g., high-intermediate-low order coupling), we implement DAS as the intermediate-order method. This method is implemented into a finite volume computational fluid dynamic (CFD) code where we see an increase in accuracy and a decrease in computational time. These benefits result from the DAS kernel admitting more admissible solutions in the intermediate step compared to the existing approach. In turn, the use of DAS allows the MOOD loop to skip the need for the lowest order cascade at many cells with discontinuities.

The second topic examines the interactions and potential damages to NASA's Mobile Launcher (ML-1 and ML-2) during Artemis missions using high-fidelity simulations. Following the damage to ML-1 during the Artemis I launch, we conducted 14 lofted vehicle simulations to understand and mitigate these effects for Artemis II. The simulations, performed with the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, evaluated acoustic and pressure conditions at key trajectory points, comparing "dry" simulations without water suppression systems to a “wet" simulation modeled using multiphase CFD. We show that, while the water systems generally reduced pressure and provided acoustic dampening, it also increased pressure in certain areas due to redirection of water caused by the plume gases. Frequency analysis validated the simulations with actual launch data, confirming the water's effectiveness in noise reduction. We then highlight hot spots and present integrated pressure statistics to help inform modifications that might need to be made on ML-2 for the Artemis II launch. Lastly, we provide a brief discussion on an interesting direction for a novel numerical method for future work.

Event Host: Christopher DeGrendele, Ph.D. Student, Applied Mathematics

Advisor: Dongwook Lee