Robust high-order space-time conservative schemes for solving conservation laws on hybrid meshes

Hua Shen, Chih-yung Wen, Kaixin Liu, Deliang Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

23 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)375-402
Number of pages28
JournalJournal of Computational Physics
Volume281
DOIs
Publication statusPublished - 5 Jan 2015

Keywords

  • High-order accuracy
  • Hybrid meshes
  • Space-time conservation element and solution element (CE/SE) method
  • Unstructured meshes

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

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