Flux-conserving treatment of non-conformal interfaces for finite-volume discretization of conservation laws

We present a new flux-conserving treatment of non-conformal mesh block interfaces for the numerical solution of conservation laws by high order finite-volume schemes. An auxiliary mesh is used at the interface to establish a connectivity between non-conformal blocks. The method does not involve any flux interpolation and conservation is therefore guaranteed by construction, without enforcing additional constraints. Additionally, several gradient reconstructions across the interface have been adapted and their order of accuracy is studied analytically and numerically. Applications to two and three dimensional fluid dynamic problems are considered, and the verification of the method is provided by comparing solutions obtained on single-block grids with no interfaces. Also the accuracy and numerical stability of the interface treatment is demonstrated empirically for a variety of test cases, such as a cylinder in supersonic cross-flow, low Mach-number vortex shedding, and a transonic turbine stage. The exemplary flow simulation problems are solved using explicit and implicit time integration schemes. The obtained results successfully demonstrate the effectiveness of the proposed method for stationary non-conformal blocks domains, as well as for mesh blocks in relative motion.