Robust multi-resolution weighted nonlinear interpolations for inter-grid boundaries in structured overset grids

In this paper, we develop a series of robust, arbitrary-location nonlinear interpolations for inter-grid boundaries in curvilinear structured overset grids for problems with strong discontinuities and complex shock reflections. In order to be capable of robustly capturing multi-discontinuities within one discretization stencil, we extend the multi-resolution weighted essentially non-oscillatory (WENO) schemes to the overset framework by developing the unequal-size nonlinear interpolations on nested sub-stencils. In addition, we also extend the freestream preserving discretization to the overset framework. The proposed methods finally offer several advantages: first, the degradation of accuracy near discontinuities can progressively reduce to first order, which ensures correct behavior in problems with multiple discontinuities in a local stencil, whereas the original WENO method only allows one discontinuity in a local stencil; second, both the linear weights and the smoothness indicators remain independent of the interpolation location, making the implementation simple and straightforward. Finally, a series of numerical test cases is carried out with strong and complex discontinuities, demonstrating the robustness of the developed method at inter-grid boundaries. Moreover, the accuracy and free-stream preservation of the multi-resolution strategy on curvilinear overset grids are also verified, showing the desired second-, fifth-, and seventh-order of accuracy and a machine zero order of freestream preservation error. Numerical experiments indicate that the nonlinear interpolations developed in this paper provide a suitable choice for structured curvilinear overset grid methods with strong and complex discontinuities.