Volume 4, Issue 5
A Third Order Conservative Lagrangian Type Scheme on Curvilinear Meshes for the Compressible Euler Equations

Juan Cheng & Chi-Wang Shu

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Commun. Comput. Phys., 4 (2008), pp. 1008-1024.

Published online: 2008-11

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  • Abstract

Based on the high order essentially non-oscillatory (ENO) Lagrangian type scheme on quadrilateral meshes presented in our earlier work [3], in this paper we develop a third order conservative Lagrangian type scheme on curvilinear meshes for solving the Euler equations of compressible gas dynamics. The main purpose of this work is to demonstrate our claim in [3] that the accuracy degeneracy phenomenon observed for the high order Lagrangian type scheme is due to the error from the quadrilateral mesh with straight-line edges, which restricts the accuracy of the resulting scheme to at most second order. The accuracy test given in this paper shows that the third order Lagrangian type scheme can actually obtain uniformly third order accuracy even on distorted meshes by using curvilinear meshes. Numerical examples are also presented to verify the performance of the third order scheme on curvilinear meshes in terms of resolution for discontinuities and non-oscillatory properties.


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@Article{CiCP-4-1008, author = {Juan Cheng and Chi-Wang Shu}, title = {A Third Order Conservative Lagrangian Type Scheme on Curvilinear Meshes for the Compressible Euler Equations}, journal = {Communications in Computational Physics}, year = {2008}, volume = {4}, number = {5}, pages = {1008--1024}, abstract = {

Based on the high order essentially non-oscillatory (ENO) Lagrangian type scheme on quadrilateral meshes presented in our earlier work [3], in this paper we develop a third order conservative Lagrangian type scheme on curvilinear meshes for solving the Euler equations of compressible gas dynamics. The main purpose of this work is to demonstrate our claim in [3] that the accuracy degeneracy phenomenon observed for the high order Lagrangian type scheme is due to the error from the quadrilateral mesh with straight-line edges, which restricts the accuracy of the resulting scheme to at most second order. The accuracy test given in this paper shows that the third order Lagrangian type scheme can actually obtain uniformly third order accuracy even on distorted meshes by using curvilinear meshes. Numerical examples are also presented to verify the performance of the third order scheme on curvilinear meshes in terms of resolution for discontinuities and non-oscillatory properties.


}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7824.html} }
TY - JOUR T1 - A Third Order Conservative Lagrangian Type Scheme on Curvilinear Meshes for the Compressible Euler Equations AU - Juan Cheng & Chi-Wang Shu JO - Communications in Computational Physics VL - 5 SP - 1008 EP - 1024 PY - 2008 DA - 2008/11 SN - 4 DO - http://dor.org/ UR - https://global-sci.org/intro/cicp/7824.html KW - AB -

Based on the high order essentially non-oscillatory (ENO) Lagrangian type scheme on quadrilateral meshes presented in our earlier work [3], in this paper we develop a third order conservative Lagrangian type scheme on curvilinear meshes for solving the Euler equations of compressible gas dynamics. The main purpose of this work is to demonstrate our claim in [3] that the accuracy degeneracy phenomenon observed for the high order Lagrangian type scheme is due to the error from the quadrilateral mesh with straight-line edges, which restricts the accuracy of the resulting scheme to at most second order. The accuracy test given in this paper shows that the third order Lagrangian type scheme can actually obtain uniformly third order accuracy even on distorted meshes by using curvilinear meshes. Numerical examples are also presented to verify the performance of the third order scheme on curvilinear meshes in terms of resolution for discontinuities and non-oscillatory properties.


Juan Cheng & Chi-Wang Shu. (1970). A Third Order Conservative Lagrangian Type Scheme on Curvilinear Meshes for the Compressible Euler Equations. Communications in Computational Physics. 4 (5). 1008-1024. doi:
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