Interpolated characteristic interface conditions for zonal grid refinement of high-order multi-block computations

When numerically calculating fluid flows around complex geometries using the high-order finite-difference method on structured grids, grid singularities are frequently observed, even if the grids are carefully generated. In multi-block computations with the generalised characteristic interface conditions (GCIC), decomposed subdomains (blocks) do not overlap but are connected by the inviscid characteristic relations. In the original theory of the GCIC, discontinuity of the metrics on the interface can be accurately treated; however, discontinuity of the grid lines on the interface is not allowed. This article proposes a theoretical extension to the GCIC by incorporating high-order interpolation methods; this extension is called GCIC with interpolation (GCIC + I). The basic concept and solution procedure of the multi-block computation with the GCIC + I are presented in detail, and two benchmark tests are conducted to validate the proposed theory.