Many portions of energy generated in the U.S. are not used and take the form of wasted heat due to a poor heat transfer efficiency. This fact leads research communities to focus on thermoelectrics as a means for using waste heat through direct thermal to electrical energy conversion. One way to enhance thermoelectric efficiency is to reduce thermal conductivity through nanostructuring. In nanostructures, understanding energy transport across the interface of two materials is important because interfaces dominate the resistance to overall thermal transport of the system and can be described by thermal boundary conductance (TBC). Also of note, an understanding of thermal transport cannot be achieved without an understanding of transfer via atomic vibration, known as phonons. In this study, two different techniques of molecular dynamics (MD) simulation are introduced in order to improve the understanding of the phonon transport at the interface of dissimilar materials and the impact of different material properties on TBC. Non-equilibrium MD simulations are used to study relative and combined contributions of mass and bond energy difference on TBC and phonon wave-packet simulations are used to obtain a detailed description of phonon interactions at the interface. At the end of this study, a simple analytical model for the prediction of effective thermal conductivity, using knowledge of thermal boundary resistance, an inverse of TBC, and the interface geometry, is developed.