A generalized adaptive central-upwind scheme for compressible flow simulations and preventing spurious vortices

Abstract

This work introduces a novel adaptive central-upwind scheme designed for simulating compressible flows with discontinuities in the flow field. The proposed approach offers significant improvements in computational efficiency over the central gradient-based reconstruction approach presented in [1] (Hoffmann, Chamarthi and Frankel, JCP 2024). By leveraging a combination of conservative and characteristic variable reconstruction, the proposed approach demonstrates oscillation-free results while effectively reducing computational costs and improving the results. Furthermore, the adaptive central-upwind algorithm is generalized to be compatible not only with the gradient-based reconstruction as in [1] but with other existing methods. In this regard, with the proposed algorithm, the standard fifth/sixth-order reconstruction scheme has also been shown to outperform existing schemes with a 20-30% reduction in computational expense with improved results. Notably, the proposed approach has successfully prevented the generation of spurious vortices in the double shear layer test cases, even with linear schemes, showcasing its robustness and effectiveness.