Orthogonal Curvilinear Coordinate Systems

2020 ◽  
pp. 89-148
Author(s):  
Gianpietro Elvio Cossali ◽  
Simona Tonini
Keyword(s):  
Coordinate Systems ◽  
Curvilinear Coordinate

scholarly journals Implementation of an Approximate Conformal UPML in 2-D DGTD

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Linqian Li ◽  
Bing Wei ◽  
Qian Yang ◽  
Debiao Ge
Keyword(s):  
Good Accuracy ◽  
Computation Time ◽  
Elliptic Cylinder ◽  
Auxiliary Equation ◽  
Coordinate Systems ◽  
Absorbing Boundary ◽  
Computational Region ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System ◽  
Absorbing Layer

Using the numerical discrete technique with unstructured grids, conformal perfectly matched layer (PML) absorbing boundary in the discontinuous Galerkin time-domain (DGTD) can be set flexibly so as to save lots of computing resources. Based on the DGTD equations in an orthogonal curvilinear coordinate system, the processes of parameter transformation for 2-D UPML between the coordinate systems of elliptical and Cartesian are given; and the expressions of transition matrix are derived. The calculation scheme of conductivity distribution in elliptic cylinder absorbing layer is given, and the calculation coefficient of DGTD in elliptic UPML is calculated. Furthermore, the 2-D iterative formulas of DGTD and that of auxiliary equation in the elliptical cylinder UPML are derived; the conformal UPML calculation in DGTD is realized. Numerical results show that very good accuracy and computational efficiency are achieved by using the method in this paper. Compared to the rectangular computational region, both the memory and computation time of conformal UPML absorbing boundary are reduced by more than 20%.

Appendix A: General Curvilinear Coordinate Systems and Higher-Order Tensors

2021 ◽  
pp. 525-572
Author(s):  
Pierre J. Carreau ◽  
Daniel C.R. De Kee ◽  
Raj P. Chhabra
Keyword(s):  
Higher Order ◽  
Coordinate Systems ◽  
Curvilinear Coordinate ◽  
Higher Order Tensors

Order of Difference Expressions in Curvilinear Coordinate Systems

1985 ◽  
Vol 107 (2) ◽  
pp. 241-250 ◽  
Author(s):  
J. F. Thompson ◽  
C. W. Mastin
Keyword(s):  
Finite Difference ◽  
Series Expansion ◽  
Uniform Grid ◽  
Coordinate Systems ◽  
Curvilinear Coordinate ◽  
Error Behavior

The order of finite difference representations on general curvilinear coordinate systems is considered in some detail. It is shown that the uniform grid order is formally preserved on the nonuniform, nonorthogonal grid in the sense of the error behavior with an increase in the number of points. However, the coefficients in the series expansion may become quite large for some point distributions. Several specific distributions are evaluated.

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