An alternative two-way coupled Euler-Lagrange scheme to model the performance of finite-size particle in supersonic flow.

• Traditional two-way coupled Euler-Lagrange(EL) underestimates the drag force and fails in supersonic flow laden finite-size particles. • An upward weighted average method is implemented for E to L coupling to well restore the actual and undisturbed gas-phase quantities acting on particles. • An upward mix-gaussian function is proposed for L to E coupling to reproduce the shock and wake zone of particle in terms of the kernel widths commended. • The modified method not only allows to track arbitrary finite-size particles, but also improves the accuracy of classical PSIC-EL in supersonic flow. In Euler-Lagrange (EL) framework, the Gauss kernel (GK) is usually introduced to avoid Dirac source disturbance of traditional particle-in-cell (PIC) method in subsonic regime. This work investigates the applicability and limitations of PIC-two-way coupling and GK for finite-size particles subjected to supersonic and dilute regime. Results indicate that the source disturbance of GK always peaks at the symmetric center of GK causing a suboptimal shock and ignoring wake in supersonic regime. Meanwhile, classical PIC-interpolation underestimates the drag force on particles due to shock and finite-size effects. To circumvent those issues, a modified coupling method utilizing upstream weighting averaged method and mix-gaussian kernel is proposed to optimize Euler-to-Lagrange coupling and Lagrange-to-Euler coupling, respectively. The modified method not only allows for accurate tracking of arbitrary finite-size particles in supersonic flows but also restores the undisturbed laden flow quantities exerting on particles. Shock and wake zone are reproduced before and after the particle based on recommended parameters. Furthermore, the modified method is validated using a particle-pair exposed to supersonic flow referred from Utkin's experiment(Utkin et al., 2021), and shows excellent agreement. Providing new insight into comprehending for two-way coupled Euler-Lagrange to simulate finite-size particles laden by supersonic flow. Dimensionless pressure and streamwise velocity using different two-way coupling methods [Display omitted] [ABSTRACT FROM AUTHOR]