  The dispersion and dissipation properties of a scheme are important to
realize high-fidelity simulations of the compressible flow, especially the
cases with broadband length scales. It has been recognized that the
minimization of dispersion error is an effective method to improve the
precision. In addition, the proper dissipation of a scheme is important to
restrain the non-physics oscillations and reserve details of flows
simultaneously. The authors have previously proposed a scale sensor to adjust
the numerical dissipation of a fourth-order finite difference scheme according
to the local scale of the flow. In this paper, the scale sensor is further
modified for the sixth-order finite difference scheme to achieve minimized
dispersion and adaptive dissipation properties. Firstly, the scale sensor
quantifies the local length scale of the numerical solution as the effective
scaled wavenumber. Then, the dispersion-dissipation condition is used to
construct the relationship between the dissipation/dispersion parameter and the
effective scaled wavenumber. Therefore, a sixth-order finite difference scheme
with minimized dispersion and adaptive dissipation (MDAD6th) is proposed.
Several benchmark test cases with broadband length scales are presented to
clarify the high resolution of the new scheme.
