The focus of this study is on serial and parallel configurations of a multistage thermoacoustic engines (TAE). Thermoacoustics integrates fluid dynamics, thermodynamics, and acoustics to explain the interactions existing between heat and sound. Considerable amounts of waste heat are released to the environment in everyday industrial processes. This waste heat cannot be reused due to its low temperature. One way for reusing some of this waste heat is to employ a thermoacoustic heat pump. TAEs can be driven by waste heat and are capable of supplying the power to drive the thermoacoustic heat pumps. However, due to the low temperature of this waste heat, single-stage TAEs cannot provide the required temperature lifts. Multistage TAEs are advantageous because they can provide sufficient temperature lifts. In this study, a computational fluid dynamics (CFD) simulation is carried out to understand the conversion process of heat to sound and study the nonlinear conjugation of unsteady heat release and acoustic disturbances. The two main parameters evaluated in this simulation are the initial pressure disturbance and the stack's temperature gradient. Their effects on actuating limit cycle oscillations are examined in a 2D numerical model. The numerical simulation results indicate that the pressure amplitude varies through alteration made in these mentioned parameters. The present numerical results are validated by previously published data.