Improved grid block interface flux reconstruction method for high-order finite difference scheme

In this study, a new method is proposed to improve the accuracy of the grid block interface flux reconstruction (IFR) approach, which was proposed by the present authors previously for numerical simulation using high order finite difference scheme. Not only is the flux at the point on the block interface corrected, but the fluxes at the adjacent points of the interface are also reconstructed with a selected correction function. This improves the accuracy of the IFR method although the biased finite difference scheme is used to compute the spatial derivatives in the interior boundary region. Four problems, including both inviscid and viscous flows, are numerically solved with the developed code to validate the accuracy of the improved IFR method. The validations imply that the new correction approach improves the accuracy of the IFR method and is effective for inviscid and viscous problems with complex geometry.