A Cartesian-to-Curvilinear Coordinate Transformation in Modified Ghost Fluid Method for Compressible Multi-Material Flows
Year: 2021
Author: Liang Xu, Hao Lou, Wubing Yang, Tiegang Liu
Communications in Computational Physics, Vol. 29 (2021), Iss. 5 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2020-0055
Communications in Computational Physics, Vol. 29 (2021), Iss. 5 : pp. 1469–1504
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 36
Keywords: Compressible multi-material flows curvilinear coordinate system modified ghost fluid method level set method multi-material Riemann problem coordinate transformation.
Author Details
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