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Curvilinear Coordinates, Local Coordinate Transformations
2019The reader probably has experience in using polar coordinates on the 2D plane, or spherical coordinates in the 3D space. Below, we consider a general treatment of curvilinear coordinate systems, which include these and many other examples.
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Curvilinear Coordinates and Curved Spaces
2018Even in flat Euclidean space it may be useful to use curvilinear coordinates; for instance, in 3d problems having central symmetry, we obtain an important simplification when the line element \(ds^2= dx^{2}+dy^{2}+dz^{2}\) is replaced by \(ds^{2}=dr^{2}+r^{2}d\theta ^{2}+r^{2}\sin ^{2}(\theta ) d\phi ^{2}.\) In a curved space we have no other choice ...
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A genuinely two-dimensional Riemann solver for compressible flows in curvilinear coordinates
Journal of Computational Physics, 2019Feng Qu, Di Sun, J. Bai, Chao Yan
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Modified couple stress theory in orthogonal curvilinear coordinates
Acta Mechanica, 2018H. Farokhi, M. Ghayesh
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