Over the last few decades, numerical simulation has fast become an effective research tool in analyzing internal and external fluid flow. Much of the unknowns associated with microscopic bounded and unbounded fluid behavior generally not obtainable via experimental approach can now be explained in details with computational fluid dynamics modeling. This has much assist designers and engineers in developing better engineering designs. However, the choice of the computational domain selected plays an important role in exhibiting the correct flow patterns associated with changes in certain parameters. This research looked at the outcomes when two computational domains were chosen to represent a system of parallel stack plates in a thermoacoustic resonator. Since the stack region is considered the “heart” of the system, accurate modeling is crucial in understanding the complex thermoacoustic solid-fluid interactions that occur. Results showed thatalthough the general flow pattern and trends have been produced with the single and double plate stack system, details of a neighboring solid wall do affect the developments of vortices in the stack region. The symmetric assumption in the computational domain may result in the absence of details that could generate an incomplete explanation of the patterns observed such as shown in this study. This is significant in understanding the solid-fluid interactions that is thermoacoustic phenomena.