Computational Fluid Dynamics (CFD) plays an important role in engineering. It allows engineers to test different designs fast; providing insight in cases where an analytical solution is not available, experimental data is difficult to obtain or is not available at all. Applications vary greatly; from the aerospace industry for the design of missiles and hypersonic vehicles to the biomedical industry for the design of artificial lungs. However, current CFD numerical techniques are neither accurate, efficient nor inexpensive. In fact, most numerical techniques lead to large errors, time-consuming grid creation methods, and many hours of High Performance Computing (HPC) resources. In addition, current solution methods do not provide unique indications of the flow physics within the solution domain. This study demonstrates the capabilities of a new scheme called Integro-Differential Scheme (IDS) [1] under realistic conditions, i.e high Reynolds and Mach number. In the attempt to accomplish this task, a new parallel IDS version is delivered capably of overcoming the current limitations of CFD. An important aspect of this research is coupling numerical solution to specially created Flow Features Extraction Functions (FFEF). These functions provide direct evidence of complex flow field interactions. This is the first attempt using cutting edge parallel libraries to validate the original serial IDS. Besides of the qualitative accuracy of this scheme, this research goes a step further using high fidelity experimental data to validate the numerical solution provided by the new parallel IDS. Further, this dissertation focuses on the solution of three complex flow interaction problems using the IDS under realistic Reynolds number conditions. The solutions obtained herein demonstrated the two most important characteristics of the IDS capabilities; its accurate physics capturing capabilities, and its efficiency when executed on HPC platforms.