비정렬 격자계에서 고차 정확도 불연속 갤러킨-다차원 공간 제한 기법을 이용한 유동 물리 해석

Abstract

The present paper deals with the continuous works of extending the multi-dimensional limiting process (MLP) for compressible flows, which has been quite successful in finite volume methods, into discontinuous Galerkin (DG) methods. From the series of the previous, it was observed that the MLP shows several superior characteristics, such as an efficient controlling of multi-dimensional oscillations and accurate capturing of both discontinuous and continuous flow features. Mathematically, fundamental mechanism of oscillation-control in multiple dimensions has been established by satisfaction of the maximum principle. The MLP limiting strategy is extended into DG framework, which takes advantage of higher-order reconstruction within compact stencil, to capture detailed flow structures very accurately. At the present, it is observed that the proposed approach yields outstanding performances in resolving non-compressive as well as compressive flow features. In the presentation, further numerical analyses and results are going to be presented to validate that the newly developed DG-MLP methods provide quite desirable performances in controlling numerical oscillations as well as capturing key flow features.