Computational accuracy and time to perform complex turbulence research remain the two critical metrics for the success of a simulation. This is more challenging for highly-turbulent and high-speed compressible flows attributing to their shock-capturing uncertainty and complex fluid-surface interactions. Recent developments in numerical techniques for high-speed compressible flows have made significant progress but often struggle to strike a balance between speed and accuracy in predicting shock-induced separations. A promising hybrid-central solver based on Pressure Implicit with Splitting of Operator for Pressure-Linked Equations (PIMPLE) algorithm and Kurganov-Tadmor (K.T). scheme addresses this issue. This paper aims to leverage modified implementation of the PIMPLE algorithm to understand the effects of transonic compressibility and shock-capturing over an aircraft wing with effective pre-conditioning and flux stabilization. Juxtaposition of flux stabilized PIMPLE algorithm with Pressure Implicit with Splitting of Operator (PISO), and Large-eddy simulations (LES) methods showcased that modified PIMPLE algorithm with corrector terms shows 9.75% faster convergence than PISO and 128% faster convergence than LES, with little to no oscillations. PIMPLE had 94% agreement with LES results for this transonic wing implementation, which can have even better improvements by altering inner and outer corrector parameters. Modified PIMPLE algorithm strikes perfect balance between accuracy and computational time. This study corroborates it as an ideal choice of solver algorithm for high-speed compressible flows over other higher-order turbulence models.