An adaptive GSM-CFD solver and its application to shock-wave boundary layer interaction

Purpose - The first purpose of this paper is to design more accurate, efficient and robust gradient smoothing methods (GSMs) for spatial derivative approximations for computational fluid dynamics (CFD) application. The second purpose is to design an adaptive GSM-CFD solver for the compressible turbulent flows, with special focus on the shock-wave boundary layer interactions. Design/methodology/approach - A new integration scheme is proposed for the node-associated GSM to improve the accuracy and robustness of the previous versions. A matrix-based algorithm and corresponding data structures are devised to improve the computational efficiency of GSM. The GSM-CFD solver is coupled with a mixed solution-based adaptive mesher to form a functional adaptive GSM-CFD solver. Findings - The improved GSMs are insensitive to mesh qualities, and can achieve high accuracy on all kinds of hybrid meshes. The adaptive GSM-CFD solver can better capture the shock wave. Originality/value - The matrix-based GSM and its corresponding data structure for improved GSM, and the development of the adaptive GSM-CFD solver for compressible turbulent flows are newly presented in this paper.