In this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method (AUSM), specifically AUSM⁺-UP [9], with high-order upwind-biased interpolation procedures, the weighted essentially non-oscillatory (WENO-JS) scheme [8] and its variations [2, 7], and the monotonicity preserving (MP) scheme [16], for solving the Euler equations. MP is found to be more effective than the three WENO variations studied. AUSM⁺-UP is also shown to be free of the so-called "carbuncle" phenomenon with the high-order interpolation. The characteristic variables are preferred for interpolation after comparing the results using primitive and conservative variables, even though they require additional matrix-vector operations. Results using the Roe flux with an entropy fix and the Lax-Friedrichs approximate Riemann solvers are also included for comparison. In addition, four reflective boundary condition implementations are compared for their effects on residual convergence and solution accuracy. Finally, a measure for quantifying the efficiency of obtaining high order solutions is proposed; the measure reveals that a maximum return is reached after which no improvement in accuracy is possible for a given grid size.