S-Space College of Engineering/Engineering Practice School (공과대학/대학원) Dept. of Mechanical Aerospace Engineering (기계항공공학부) Journal Papers (저널논문_기계항공공학부)
Higher-order multi-dimensional limiting strategy for discontinuous Galerkin methods in compressible inviscid and viscous flows
- Park, Jin Seok; Kim, Chongam
- Issue Date
- Computers and Fluids, Vol.96, pp. 377-396
- 공학; Multi-dimensional limiting process; Multi-dimensional limiting condition; Higher-order methods; Discontinuous Galerkin methods; Unstructured grids; Compressible flows
- This paper deals with the multi-dimensional limiting process (MLP) for discontinuous Galerkin (DG) methods to compute compressible inviscid and viscous flows. The MLP, which has been quite successful in finite volume methods (FVM), is extended to DG methods for hyperbolic conservation laws. In previous works, the MLP was shown to possess several superior characteristics, such as the ability to control multidimensional oscillation efficiently and to capture both discontinuous and continuous multi-dimensional flow features accurately within the finite volume framework. In particular, the oscillation-control mechanism in multiple dimensions was established by combining the local maximum principle and the multidimensional limiting (MLP) condition, leading to the formulation of efficient and accurate MLP-u slope limiters.The MLP limiting strategy is now extended to the higher-order DG framework to develop the hierarchical MLP formulation on unstructured grids, which facilitates the capturing of compressible flow structures very accurately. By combining the behavior of local extrema with the augmented MLP condition, the hierarchical MLP method (the MLP-based troubled-cell markers and the MLP limiters in the RKDG formulation) is developed for arbitrary DG-Pn polynomial approximations. Through extensive numerical analyses and computations on unstructured grids, it is demonstrated that the proposed hierarchical DG-MLP method yields outstanding performance in resolving non-compressive as well as compressive flow features. (C) 2013 Elsevier Ltd. All rights reserved.
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