Investigation of Multiresolution Weighted Compact Nonlinear Schemes on Curvilinear Meshes

A seventh-order multiresolution weighted compact nonlinear scheme (MR-WCNS) is developed for simulating various flow problems on curvilinear meshes. The scheme incorporates the idea of the multiresolution weighted essentially non-oscillatory scheme (MR-WENO) scheme for node-to-midpoint nonlinear interpolation, performing the weighting procedure over nested central stencils rather than equal-width stencils used in traditional methods. To ensure robustness and accuracy in complex geometries, this scheme is implemented alongside the symmetrical conservative metric method. Additionally, the fifth-order MR-WCNS from our previous work is extended to curvilinear grids using the same framework. The performance of both schemes is systematically evaluated by solving inviscid, viscous, and turbulent flows governed by the Euler, Navier–Stokes, and Reynolds-averaged Navier–Stokes equations. The results demonstrate excellent agreement with reference data, validating the methods’ technical reliability. Compared to a conventional second-order MUSCL scheme, both MR-WCNSs deliver superior accuracy and computational efficiency across a range of cases, from academic benchmarks to practical applications. Between the two, the seventh-order MR-WCNS outperforms its fifth-order counterpart in terms of accuracy, resolution, and computational efficiency. These findings highlight the strong potential of MR-WCNSs for engineering applications.