High-order alternative finite difference scheme with minimized dispersion and adaptive dissipation for solving compressible flows

Numerical schemes with good spectral properties are of significance in simulating compressible flows with broad-scale flow structures. In the present article, we propose the AMDAD-ACU FD (Finite Difference) scheme, an Alternative formulation of the ACU (Adjustable Central-Upwind) FD scheme with MDAD (Minimized Dispersion and Adaptive Dissipation) property, for solving compressible flows. In the smooth flow field, the AMDAD-ACU FD scheme will degenerate into the AMDAD (Alternative formulation of MDAD) FD scheme, an Alternative formulation of the linear FD scheme with MDAD property, to resolve broad-scale flow structures with high resolution. While in the vicinity of discontinuities, the AMDAD-ACU FD scheme will be adjusted to the AMDAD-CU FD scheme, an Alternative formulation of the nonlinear CU (Central-Upwind) FD scheme with MDAD property, to capture shock waves and/or contact discontinuities without spurious oscillations. Therefore, the proposed AMDAD-ACU FD scheme is suitable for solving compressible flows with broad-scale flow structures and/or discontinuities. Several benchmark cases are numerically tested to demonstrate the accuracy, high resolution, and robustness of the proposed AMDAD-ACU FD scheme in solving compressible flows.