In implicit schemes, for steady-state problems, the explicit operator determines how accurate the numerical solution is and the implicit operator determines how fast the solution converges to a steady-state solution. We investigate for an optimal combination of implicit and explicit operators to achieve accuracy and efficiency simultaneously using the AUSM family of schemes. LU-SGS schemes are efficient for steady-state problems but not accurate for time-dependent problems. We propose a modified LU-SGS scheme to get an accurate solution for time-dependent problems. We use the flow over a blunt body for supersonic and hypersonic inlet Mach numbers as a test case for steady-state problems and
isentropic vortex problems as a test case for time-dependent problems.