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Chongam Kim

2013-11-11
15:40:00 - 17:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

The present seminar deals with the multi-dimensional limiting process (MLP) on unstructured grids to compute compressible flows. Compared with traditional limiting strategies, such as TVD or ENO-type schemes, MLP effectively controls unwanted oscillations particularly in multiple dimensions. Especially, this oscillation-control mechanism has been established by combining the local maximum principle and the multi-dimensional limiting (MLP) condition, which leads to the formulation of the efficient and accurate MLP-u slope limiters. Recently, this limiting philosophy is hierarchically extended into higher-order Pn approximation. The resulting algorithm, called the hierarchical MLP, facilitates the accurate capturing of detailed flow structures in both continuous and discontinuous regions. This algorithm has been developed in the modal discontinuous Galerkin (DG) framework, but it also can be formulated into a nodal framework, most notably the correction procedure via reconstruction (CPR) framework. Troubled-cells are detected within the MLP concept, and then the projection procedure and MLP slope limiter adjust sub-cell distributions. Through extensive numerical analyses and computations on unstructured grids, it is demonstrated that the proposed method yields outstanding performance in resolving non-compressive as well as compressive flow features.

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