Generalized Characteristic Interface Conditions for Accurate Multi-Block Computation

Abstract

In a practical computation with a structured grid around a complex body, singular points can be frequently found where an abrupt grid change exists. The grid singularity poses a troublesome problem when some finite difference scheme with high accuracy and resolution is applied. An excellent theory has been proposed, which solve the above singular problem by decomposing a computational domain into two blocks along a line or a surface which contains the singular points and by imposing accurate characteristic-based interface conditions at the block interface. However, the original theory has a limitation on the combination between the adjacent computational coordinate definitions. Concretely, these two coordinates have to be the same direction on the block interface. For a flexible coordinate arrangement without the restriction, the original characteristic-based interface treatment is extended and generalized. Consequently, the coincidence of the computational coordinate definitions becomes unnecessary, and a more flexible multi-block computation can be realized successfully. Numerical test analysis of vortex convection is performed for validation of the new theory, and excellent performance is confirmed as a result.