Extending Weighted Compact Nonlinear Schemes to Complex Grids with Characteristic-Based Interface Conditions

There are still some challenges, such as grid quality, numerical stability, and boundary schemes, in the practical application of high-order finite difference schemes for complex configurations This study presents some improved strategies that indicate potential engineering applications of high-order schemes The formally fifth-order weighted compact nonlinear scheme developed by the authors is implemented on point Matched multiblock structured grids, which are generated over complex configurations to ensure the grid quality of each component block The information transmission between neighboring blocks is carried Out by new characteristic-based interface conditions that directly exchange the spatial derivatives on each side of an interface by means of a characteristic-based projection to keep the high-order accuracy and high resolution of a spatial difference scheme The high-order scheme combined with the interface conditions is shown to be asymptotically stable The engineering-oriented applications of the high-order strategy are demonstrated by solving several two- and three'-dimensional problems with complex grid systems