Hierarchical multi-dimensional limiting strategy for correction procedure via reconstruction

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• 作者：Jin Seok Park^a ; Chongam Kim^b ; ^{chongam@snu.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Multi-dimensional limiting process (MLP) ; Flux reconstruction or correction procedure via reconstruction (FR/CPR) ; Higher-order methods ; Unstructured grids ; Shock capturing
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：308
• 期：Complete
• 页码：57-80
• 全文大小：4872 K

文摘

Hierarchical multi-dimensional limiting process (MLP) is improved and extended for flux reconstruction or correction procedure via reconstruction (FR/CPR) on unstructured grids. MLP was originally developed in finite volume method (FVM) and it provides an accurate, robust and efficient oscillation-control mechanism in multiple dimensions for linear reconstruction. This limiting philosophy can be hierarchically extended into higher-order Pn approximation or reconstruction. The resulting algorithm is referred to as the hierarchical MLP and facilitates detailed capture of flow structures while maintaining formal order-of-accuracy in a smooth region and providing accurate non-oscillatory solutions across a discontinuous region. This algorithm was developed within modal DG framework, but it can also be formulated into a nodal framework, most notably the FR/CPR framework. Troubled-cells are detected by applying the MLP concept, and the final accuracy is determined by a projection procedure and the hierarchical MLP limiting step. Extensive numerical analyses and computations, ranging from two-dimensional to three-dimensional fluid systems, have demonstrated that the proposed limiting approach yields outstanding performances in capturing compressible inviscid and viscous flow features.