scholarly journals Application of a Steady Meandering River with Piers Using a Lattice Boltzmann Sub-Grid Model in Curvilinear Coordinate Grid

Water ◽  
2018 ◽  
Vol 10 (5) ◽  
pp. 615
Author(s):  
Liping Chen ◽  
Zhuangming Zhao ◽  
Ping Huang
Keyword(s):  
Lattice Boltzmann ◽  
Meandering River ◽  
Coordinate Grid ◽  
Grid Model ◽  
Curvilinear Coordinate

Curvilinear coordinate lattice Boltzmann simulation for necklace-ring beams in the nonlinear Schrödinger equation

2020 ◽  
Vol 31 (10) ◽  
pp. 2050136
Author(s):  
Boyu Wang ◽  
Jianying Zhang ◽  
Guangwu Yan
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Lattice Boltzmann ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Time Derivative ◽  
Three Dimensional ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Curvilinear Coordinate

Necklace-ring solitons have gained much attention due to their potential applications in optics and other scientific areas. In this paper, the numerical investigation of the nonlinear Schrödinger equation by using the curvilinear coordinate lattice Boltzmann method is proposed to study necklace-ring solitons. Different from those used in the general curvilinear coordinate lattice Boltzmann models, the lattices used in this work are uniform in two- and three-dimensional space. Furthermore, the model contains spatial evolution rather than time evolution to avoid the complexity of dealing with higher-order time derivative terms as well as to maintain the simplicity of the algorithm. Numerical experiments reproduce the evolution of two- and three-dimensional necklace-ring solitons. The truncation error analysis indicates that our model is equivalent to the Crank–Nicolson difference scheme.

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