Generalized characteristic interface conditions for high-order multi-block computation

Abstract

In practical fluid computation with structured grids around complex geometries, singular points with metric discontinuity can frequently be found. Generally, the grid singularities may cause numerical oscillations when some high-order finite difference scheme is applied. Recently, an excellent theory has been proposed which solves the above singular problem by block decomposition along the singular surface and by imposition of the characteristic interface conditions (CIC) on the block interface. However, the original theory has constraints on the mathematical treatment of the block interface, and therefore prevents numerical flexibility from a practical point of view. In this article, in order to extend the functions of the original CIC, we propose the generalized characteristic interface conditions (GCIC). Proper numerical test analysis is conducted to validate the performance of the GCIC, and as a practical application, multi-block computation is performed with the GCIC applied to complex geometry.