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

Mass transport in water waves over an elastic bed

1995 ◽  
Vol 450 (1939) ◽  
pp. 371-390 ◽  
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Mass Transport ◽  
Water Waves ◽  
Viscous Boundary Layer ◽  
Curvilinear Coordinate ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Orthogonal Curvilinear Coordinate System ◽  
Viscous Boundary

The mass transport velocity in water waves propagating over an elastic bed is investigated. Water is assumed to be incompressible and slightly viscous. The elastic bed is also incompressible and satisfies the Hooke’s law. For a small amplitude progressive wave perturbation solutions via a boundary-layer approach are obtained. Because the wave amplitude is usually larger than the viscous boundary layer thickness and because the free surface and the interface between water and the elastic bed are moving, an orthogonal curvilinear coordinate system (Longuet-Higgins 1953) is used in the analysis of free surface and interfacial boundary layers so that boundary conditions can be applied on the actual moving surfaces. Analytical solutions for the mass transport velocity inside the boundary layer adjacent to the elastic seabed and in the core region of the water column are obtained. The mass transport velocity above a soft elastic bed could be twice of that over a rigid bed in the shallow water.

A 2D Numerical Model for Simulation of Two-Dimensional Circular Dam-Break

2011 ◽  
Vol 130-134 ◽  
pp. 2993-2996
Author(s):  
Ming Qin Liu ◽  
Y.L. Liu
Keyword(s):  
Solution Procedure ◽  
Dam Break ◽  
Curvilinear Coordinates ◽  
Two Dimensional ◽  
Proposed Model ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System ◽  
Orthogonal Curvilinear Coordinates ◽  
Averaged Model ◽  
The Mathematical Model

The purpose of this paper is to present a 2D depth-averaged model under orthogonal curvilinear coordinates for simulating two-dimensional circular dam-break flows. The proposed model uses an orthogonal curvilinear coordinate system efficiently and accurately to simulate the flow field with irregular boundaries. As for the numerical solution procedure, The SIMPLEC solution procedure has been used for the transformed governing equations in the transformed domain. Practical application of the model is illustrated by an example, which demonstrates that the mathematical model can capture hydraulic discontinuities accurately such as steep fronts, hydraulic jump and drop, etc.

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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