Volume 29, Issue 5
A Cartesian-to-Curvilinear Coordinate Transformation in Modified Ghost Fluid Method for Compressible Multi-Material Flows

Liang Xu, Hao Lou, Wubing Yang & Tiegang Liu

Commun. Comput. Phys., 29 (2021), pp. 1469-1504.

Published online: 2021-03

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  • Abstract

Modified ghost fluid method (MGFM) provides us an effective manner to simulate compressible multi-material flows. In most cases, the applications are limited in relatively simple geometries described by Cartesian grids. In this paper, the MGFM treatment with the level set (LS) technique is extended to curvilinear coordinate systems. The chain rule of differentiation (applicable to general curvilinear coordinates) and the orthogonal transformation (applicable to orthogonal curvilinear coordinates) are utilized to deduce the Cartesian-to-curvilinear coordinate transformation, respectively. The relationship between these two transformations for the extension of the LS/MGFM algorithm is analyzed in theory. It is shown that these two transformations are equivalent for orthogonal curvilinear grids. The extension of the LS/MGFM algorithm using the chain rule has a wider range of applications, as there is essentially no requirement for the orthogonality of the grids. Several challenging problems in two- or three-dimensions are utilized to validate the developed algorithm in curvilinear coordinates. The results indicate that this algorithm enables a simple and effective implementation for simulating interface evolutions, as in Cartesian coordinate systems. It has the potential to be applied in more complex computational domains.

  • Keywords

Compressible multi-material flows, curvilinear coordinate system, modified ghost fluid method, level set method, multi-material Riemann problem, coordinate transformation.

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@Article{CiCP-29-1469, author = {Xu , Liang and Lou , Hao and Yang , Wubing and Liu , Tiegang}, title = {A Cartesian-to-Curvilinear Coordinate Transformation in Modified Ghost Fluid Method for Compressible Multi-Material Flows}, journal = {Communications in Computational Physics}, year = {2021}, volume = {29}, number = {5}, pages = {1469--1504}, abstract = {

Modified ghost fluid method (MGFM) provides us an effective manner to simulate compressible multi-material flows. In most cases, the applications are limited in relatively simple geometries described by Cartesian grids. In this paper, the MGFM treatment with the level set (LS) technique is extended to curvilinear coordinate systems. The chain rule of differentiation (applicable to general curvilinear coordinates) and the orthogonal transformation (applicable to orthogonal curvilinear coordinates) are utilized to deduce the Cartesian-to-curvilinear coordinate transformation, respectively. The relationship between these two transformations for the extension of the LS/MGFM algorithm is analyzed in theory. It is shown that these two transformations are equivalent for orthogonal curvilinear grids. The extension of the LS/MGFM algorithm using the chain rule has a wider range of applications, as there is essentially no requirement for the orthogonality of the grids. Several challenging problems in two- or three-dimensions are utilized to validate the developed algorithm in curvilinear coordinates. The results indicate that this algorithm enables a simple and effective implementation for simulating interface evolutions, as in Cartesian coordinate systems. It has the potential to be applied in more complex computational domains.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0055}, url = {http://global-sci.org/intro/article_detail/cicp/18723.html} }
TY - JOUR T1 - A Cartesian-to-Curvilinear Coordinate Transformation in Modified Ghost Fluid Method for Compressible Multi-Material Flows AU - Xu , Liang AU - Lou , Hao AU - Yang , Wubing AU - Liu , Tiegang JO - Communications in Computational Physics VL - 5 SP - 1469 EP - 1504 PY - 2021 DA - 2021/03 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2020-0055 UR - https://global-sci.org/intro/article_detail/cicp/18723.html KW - Compressible multi-material flows, curvilinear coordinate system, modified ghost fluid method, level set method, multi-material Riemann problem, coordinate transformation. AB -

Modified ghost fluid method (MGFM) provides us an effective manner to simulate compressible multi-material flows. In most cases, the applications are limited in relatively simple geometries described by Cartesian grids. In this paper, the MGFM treatment with the level set (LS) technique is extended to curvilinear coordinate systems. The chain rule of differentiation (applicable to general curvilinear coordinates) and the orthogonal transformation (applicable to orthogonal curvilinear coordinates) are utilized to deduce the Cartesian-to-curvilinear coordinate transformation, respectively. The relationship between these two transformations for the extension of the LS/MGFM algorithm is analyzed in theory. It is shown that these two transformations are equivalent for orthogonal curvilinear grids. The extension of the LS/MGFM algorithm using the chain rule has a wider range of applications, as there is essentially no requirement for the orthogonality of the grids. Several challenging problems in two- or three-dimensions are utilized to validate the developed algorithm in curvilinear coordinates. The results indicate that this algorithm enables a simple and effective implementation for simulating interface evolutions, as in Cartesian coordinate systems. It has the potential to be applied in more complex computational domains.

Liang Xu, Hao Lou, Wubing Yang & Tiegang Liu. (2021). A Cartesian-to-Curvilinear Coordinate Transformation in Modified Ghost Fluid Method for Compressible Multi-Material Flows. Communications in Computational Physics. 29 (5). 1469-1504. doi:10.4208/cicp.OA-2020-0055
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