Multi-dimensional Limiting Strategy for Higher-order CFD Methods - Progress and Issue (Invited)

The present paper deals with the progress of multi-dimensional limiting process (MLP) and discuss the issues for further improvements. MLP, which has been originally developed in finite volume method (FVM), provides an accurate, robust and efficient oscillationcontrol mechanism in multiple dimensions for linear reconstruction. This limiting philosophy can be hierarchically extended into higher-order Pn approximation or reconstruction. The resulting algorithm, called the hierarchical MLP, facilitates the capturing of detailed flow structures while maintaining the formal order-of-accuracy in smooth region and providing accurate non-oscillatory solutions across discontinuous region. This algorithm has been developed within the modal DG framework, but it also can be formulated into a nodal framework, most notably the CPR framework. Troubled-cells are detected by applying the MLP concept, and the final accuracy is determined by the projection procedure and the hierarchical MLP limiting step. Through extensive numerical analyses and computations ranging from scalar conservation laws to fluid systems, it is demonstrated that the proposed limiting approach yields the outstanding performances in capturing compressible inviscid and viscous flow features. Further issues are also mentioned to improve and extend the current approach for higher-order simulations of high-Reynolds number compressible flows.Authors appreciate the financial supports by the EDISON program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2011-0020559) and by NSL (National Space Laboratory) program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2014M1A3A3A02034856). This work is also partially supported by the RoK ST&R project of Lockheed Martin Corporation. Authors also appreciate the computing resources provided by the KISTI Supercomputing Center(KSC-2014-C3-054).OAIID:RECH_ACHV_DSTSH_NO:420150000004648007RECH_ACHV_FG:RR00200003ADJUST_YN:EMP_ID:A001138CITE_RATE:FILENAME:6.2015-3199.pdfDEPT_NM:기계항공공학부EMAIL:chongam@snu.ac.krSCOPUS_YN:FILEURL:https://srnd.snu.ac.kr/eXrepEIR/fws/file/a984d649-4b23-435b-adc9-df9aa0c8aa46/linkCONFIRM: