Since environmental sustainability and climate change are fundamental challenges of our times, thermoacoustic Stirling Engines are getting attention because of its potential to address these highly relevant and critical issues. Thermoacoustic engines have the advantage of being an inexpensive and robust device that has no moving parts, therefore has the versatility to extract energy from a wide variety of heat sources ranging from waste heat from power plants to exhaust heat of vehicles, and in the process reduce fossil fuel emissions. In this article, our investigation involves simulations for both traveling wave and standing wave thermoacoustic engines. For traveling wave thermoacoustic engines, the acoustic waves generated from the heat source is a traveling wave in a closed loop while for a standing wave thermoacoustic engine the acoustic waves are standing waves confined within a straight tube. The frequencies and amplitudes of the acoustic pressure waves are a function of the geometries of the tubes, heat exchangers and stacks. For this study, we use a coupled PowerFLOW™ and PowerTHERM™ methodology to simulate the buoyancy driven flows that generate acoustic pressure waves. We compared the simulation results for both the traveling and standing wave thermoacoustic engines with test data and did observe good correlation for both the cases and investigate design changes as well. Therefore, we demonstrate that simulation workflows are an important step forward in the design and optimization of thermoacoustic engines.