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Thesis (Ph. D.)--University of Rochester. Department of Mechanical Engineering, 2022., Performance degradation in laser direct-drive (LDD) inertial confinement fusion (ICF) implosions is caused by several effects, including Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) hydrodynamic instability growth. RT instability growth occurs in both the acceleration and deceleration phases of implosions. The first half of this thesis examines the evolution of internal perturbations that create seeds for instability growth during shock-transit (or early-time), while the second half describes the perturbation evolution during shell deceleration. During shock-transit, perturbations from shell material density modulations and isolated defects plant seeds at various interfaces such as the ablation front and material interfaces. These seeds can become amplified due to secular feedout growth and shock-induced vorticity and will grow exponentially during the acceleration phase due to ablative RT. A comprehensive understanding of this evolution is essential to characterize the impact of internal defects on inflight shell integrity. Through detailed simulations and analysis, this thesis identifies several key physical processes that play a role in the evolution of perturbations created by these defects throughout the early stage of implosions. Simulations also predict that significant shell mass modulations develop during shell acceleration. The use of low density ablator materials (foam) is suggested as a potential mitigation strategy to reduce the effects created by these defects. To perform this detailed study of internal defect evolution, two new high-fidelity physics codes were developed to track characteristic wave propagation in the ICF context using low-noise, low-dissipation, high-order spatial accuracy solution methods. Modern high performance computing (HPC) systems have becoming increasingly complex, and adapting existing or new software to fully utilize them is a significant development challenge. Each code in this thesis examines the feasibility of differen