scholarly journals Finite difference solutions for nonlinear water waves using an immersed boundary method

2020 ◽  
Author(s):  
Yan Xu ◽  
Harry B. Bingham ◽  
Yanlin Shao
Keyword(s):  
Finite Difference ◽  
Immersed Boundary Method ◽  
Water Waves ◽  
Immersed Boundary ◽  
Nonlinear Water Waves ◽  
Boundary Method

Two-dimensional compact finite difference immersed boundary method

2011 ◽  
Vol 65 (6) ◽  
pp. 609-624 ◽  
Author(s):  
Paulo J. S. A. Ferreira de Sousa ◽  
José C. F. Pereira ◽  
James J. Allen
Keyword(s):  
Finite Difference ◽  
Immersed Boundary Method ◽  
Immersed Boundary ◽  
Two Dimensional ◽  
Compact Finite Difference ◽  
Boundary Method

scholarly journals An immersed boundary method with iterative symmetric interpolation for irregular surface topography in seismic wavefield modelling

2020 ◽  
Author(s):  
Xiang Li ◽  
Gang Yao ◽  
Fenglin Niu ◽  
Di Wu
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Surface Topography ◽  
Immersed Boundary Method ◽  
Acoustic Waves ◽  
Interpolation Method ◽  
Immersed Boundary ◽  
Boundary Method ◽  
Wavefield Simulation ◽  
Irregular Free Surface

Abstract The irregular free surface topography has a significant impact on simulations of seismic wave propagation. Therefore, an accurate representation of the irregular free surface is required for an accurate wavefield simulation. We propose an immersed boundary method used in fluid dynamics calculation to simulate acoustic waves with finite-difference in media with irregular surfaces. First, we set the number of ghost layers to half the length of the finite-difference stencil. Then, we define mirror points by orthogonally projecting the ghost points to fractional points below the free surface. We calculate the wavefield at these mirror points using an iterative symmetric interpolation method. Finally, we set the wavefield at the ghost points to the negative value of the wavefield of their corresponding mirror points. The proposed iterative symmetric interpolation method allows computing the wavefield at the mirror points more accurately and stably than the conventional immersed boundary methods. Numerical examples validate the accuracy and stability of this method in seismic forward modelling with strongly varying topography.

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