A high-resolution,hybrid compact-WENO scheme with minimized dispersion and controllable dissipation

In this paper, a high-resolution, hybrid compact-WENO scheme is developed based on the minimized dispersion and controllable dissipation reconstruction technique. Firstly, a sufficient condition for a family of tri-diagonal compact schemes to have independent dispersion and dissipation is derived. Then, a specific 4th order compact scheme with low dispersion and adjustable dissipation is constructed and analyzed. Finally, the optimized compact scheme is blended with the WENO scheme to form the hybrid scheme. Moreover, the approximation dispersion relation approach is employed to optimize the spectral properties of the nonlinear scheme to yield the true wave propagation behavior of the finite difference scheme. Several test cases are carried out to verify the high-resolution as well as the robust shock-capturing capabilities of the proposed scheme.