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Title: Robust high-order space-time conservative schemes for solving conservation laws on hybrid meshes
Authors: Shen, H
Wen, CY 
Liu, KX
Zhang, DL
Keywords: Space-time conservation element and solution element (CE/SE) method
High-order accuracy
Hybrid meshes
Unstructured meshes
Issue Date: 2015
Publisher: Academic Press
Source: Journal of computational physics, 2015, v. 281, p. 375-402 How to cite?
Journal: Journal of computational physics 
Abstract: In this paper, the second-order space-time conservation element and solution element (CE/SE) method proposed by Chang (1995) [3] is implemented on hybrid meshes for solving conservation laws. In addition, the present scheme has been extended to high-order versions including third and fourth order. Most methodologies of proposed schemes are consistent with that of the original CE/SE method, including: (i) a unified treatment of space and time (thereby ensuring good conservation in both space and time); (ii) a highly compact node stencil (the solution node is calculated using only the neighboring mesh nodes) regardless of the order of accuracy at the cost of storing all derivatives. A staggered time marching strategy is adopted and the solutions are updated alternatively between cell centers and vertexes. To construct explicit high-order schemes, second and third-order derivatives are calculated by a modified finite-difference/weighted-average procedure which is different from that used to calculate the first-order derivatives. The present schemes can be implemented on a wide variety of meshes, including triangular, quadrilateral and hybrid (consisting of both triangular and quadrilateral elements). Beyond that, it can be easily extended to arbitrary-order schemes and arbitrary shape of polygonal elements by using the present methodologies. A series of common benchmark examples are used to confirm the accuracy and robustness of the proposed schemes. .
ISSN: 0021-9991
DOI: 10.1016/
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