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Volume 34, Issue 1
Symmetry Preservation by a Compatible Staggered Lagrangian Scheme Using the Control-Volume Discretization Method in $r–z$ Coordinate

Chunyuan Xu & Qinghong Zeng

DOI: 10.4208/cicp.OA-2022-0085

Commun. Comput. Phys., 34 (2023), pp. 38-64.

Published online: 2023-08

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  • Abstract

This paper aims at developing a control volume staggered Lagrangian scheme in $r–z$ coordinate that preserves symmetry property. To achieve this goal, the support operator method is first utilized to derive the compatible discretization that satisfies the Geometrical Conservation Law (GCL) and momentum and total energy conservation property. We further introduce a method of source term treatment to recover the spherical symmetry of the current scheme. It is shown that the developed scheme has the benefit of maintaining the momentum and total energy conservation. The equi-angular grid, randomly distorted polar grid, and Cartesian grid are considered for one-dimensional spherical flow simulations. Also, an extension to the non-spherical flow is presented. The results confirm the good performance of the developed scheme.

  • Keywords

Symmetry preservation, compatibility, control-volume scheme, staggered Lagrangian scheme.

  • AMS Subject Headings

65M08, 76M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-34-38, author = {Xu , Chunyuan and Zeng , Qinghong}, title = {Symmetry Preservation by a Compatible Staggered Lagrangian Scheme Using the Control-Volume Discretization Method in $r–z$ Coordinate}, journal = {Communications in Computational Physics}, year = {2023}, volume = {34}, number = {1}, pages = {38--64}, abstract = {

This paper aims at developing a control volume staggered Lagrangian scheme in $r–z$ coordinate that preserves symmetry property. To achieve this goal, the support operator method is first utilized to derive the compatible discretization that satisfies the Geometrical Conservation Law (GCL) and momentum and total energy conservation property. We further introduce a method of source term treatment to recover the spherical symmetry of the current scheme. It is shown that the developed scheme has the benefit of maintaining the momentum and total energy conservation. The equi-angular grid, randomly distorted polar grid, and Cartesian grid are considered for one-dimensional spherical flow simulations. Also, an extension to the non-spherical flow is presented. The results confirm the good performance of the developed scheme.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0085}, url = {http://global-sci.org/intro/article_detail/cicp/21879.html} }
TY - JOUR T1 - Symmetry Preservation by a Compatible Staggered Lagrangian Scheme Using the Control-Volume Discretization Method in $r–z$ Coordinate AU - Xu , Chunyuan AU - Zeng , Qinghong JO - Communications in Computational Physics VL - 1 SP - 38 EP - 64 PY - 2023 DA - 2023/08 SN - 34 DO - http://doi.org/10.4208/cicp.OA-2022-0085 UR - https://global-sci.org/intro/article_detail/cicp/21879.html KW - Symmetry preservation, compatibility, control-volume scheme, staggered Lagrangian scheme. AB -

This paper aims at developing a control volume staggered Lagrangian scheme in $r–z$ coordinate that preserves symmetry property. To achieve this goal, the support operator method is first utilized to derive the compatible discretization that satisfies the Geometrical Conservation Law (GCL) and momentum and total energy conservation property. We further introduce a method of source term treatment to recover the spherical symmetry of the current scheme. It is shown that the developed scheme has the benefit of maintaining the momentum and total energy conservation. The equi-angular grid, randomly distorted polar grid, and Cartesian grid are considered for one-dimensional spherical flow simulations. Also, an extension to the non-spherical flow is presented. The results confirm the good performance of the developed scheme.

Chunyuan Xu & Qinghong Zeng. (2023). Symmetry Preservation by a Compatible Staggered Lagrangian Scheme Using the Control-Volume Discretization Method in $r–z$ Coordinate. Communications in Computational Physics. 34 (1). 38-64. doi:10.4208/cicp.OA-2022-0085
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