A high-resolution finite volume scheme based on optimal spectral properties of the fully discrete scheme with minimized dispersion and adaptive dissipation

Abstract

For the compressible flows with broadband length scales, a high-resolution scheme based on the finite volume method with minimized dispersion and adaptive dissipation is proposed, which is capable of capturing the small-scale flow details and discontinuities. Firstly, the dispersion property is optimized for the fully discrete scheme, and the minimized dispersion parameters for different Courant numbers are obtained. Then, the dispersion-dissipation condition and a scale sensor are employed to get the critical dissipation parameter which not only can suppressed the numerical oscillations but also can keep the dissipation as low as possible to capture more flow details. Moreover, the critical dissipation isosurface is constructed to develop the functional relationship between the dissipation and the estimated scaled wavenumber. To have the capability of capturing shock waves, the proposed scheme is blended with the optimized WENO-Z scheme to form the hybrid scheme. Finally, several benchmark test cases are employed to verify the high-resolution properties and the robustness of the scheme proposed in the present paper. Futhermore, more high-fidelity solutions obtained by the proposed scheme for some numerical simulations with complex geometric configurations are expected.