Non-matching grid interface treatment for the space-time conservation element and solution element method

Abstract

A conservative interface treatment for multi-block computation on structured quadrilateral grids using the space-time conservation element and solution element (CE/SE) method has been developed. In the CE/SE method, space and time are considered as a single entity, and both local and global flux conservation are preserved in the solution procedure. Thus, accurate and computationally-efficient numerical solutions can be achieved. However, if this method is applied to non-matching multi-block computational cases to evaluate the unsteadiness of the interaction, the space-time flux balance at the interface will be broken up. To resolve this problem, a novel technique is proposed for the exchange of information between the two sides of the interface. In this approach, Sub-conservation element, sub-solution element and local space-time conservation conditions near the interface can be established elaborately. Moreover, by taking full advantage of key concepts of the CE/SE method, it can enforce flux conservation across an interface between different blocks in a simple and efficient manner. Numerical experiments showed that, for a variety of flow problems involving oblique shock reflection, and laminar flow inside a lid-driven cavity, the interface treatment is valid to establish communications between two different blocks with preserving high-accuracy of CE/SE method and no discontinuity of any computed variable or pressure reflection occurred at this numerical interface.