THE COMPARISON OF WEIGHTED COMPACT SCHEMES AND WENO SCHEME

Linear compact scheme and weighted essentially non-oscillatory(WENO) scheme are two typical high order numerical schemes.They have their own merits and drawbacks.Linear compact scheme has high order accuracy order, high resolution and low dissipation, which is a nice numerical scheme for multi-scale flow.However, it can not compute the flow with strong shock wave.WENO scheme is a robust high order shock capturing scheme.But the dissipation is high.The resolution for short wave is not ideal.In recent years, a series of weighted compact schemes were developed by the combination of linear compact scheme and WENO scheme.In this paper, we systematically compare the properties of weighted compact schemes and WENO scheme including the construction, the capability to capture strong shock wave, the resolution, the convergence and paralleling efficiency.Our study shows that weighted compact schemes have no obvious superiority in the computation of aerodynamics to WENO scheme.