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 - <p style="text-align: justify;">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.</p>