Leading-order cross term correction of three-dimensional parabolic equation models

2016 ◽  
Vol 139 (1) ◽  
pp. 263-270 ◽  
Author(s):  
Frédéric Sturm
Keyword(s):  
Parabolic Equation ◽  
Three Dimensional ◽  
Leading Order ◽  
Cross Term

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

Underwater acoustic energy fluctuations during strong internal wave activity using a three-dimensional parabolic equation model

2019 ◽  
Vol 146 (3) ◽  
pp. 1875-1887 ◽  
Author(s):  
Georges A. Dossot ◽  
Kevin B. Smith ◽  
Mohsen Badiey ◽  
James H. Miller ◽  
Gopu R. Potty
Keyword(s):  
Parabolic Equation ◽  
Internal Wave ◽  
Three Dimensional ◽  
Equation Model ◽  
Wave Activity ◽  
Acoustic Energy ◽  
Underwater Acoustic

scholarly journals Combination of the Improved Diffraction Nonlocal Boundary Condition and Three-Dimensional Wide-Angle Parabolic Equation Decomposition Model for Predicting Radio Wave Propagation

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Ruidong Wang ◽  
Guizhen Lu ◽  
Rongshu Zhang ◽  
Weizhang Xu
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Parabolic Equation ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Three Dimensional ◽  
Wide Angle ◽  
Computational Accuracy ◽  
Decomposition Model ◽  
Convolution Integrals

Diffraction nonlocal boundary condition (BC) is one kind of the transparent boundary condition which is used in the finite-difference (FD) parabolic equation (PE). The greatest advantage of the diffraction nonlocal boundary condition is that it can absorb the wave completely by using one layer of grid. However, the speed of computation is low because of the time-consuming spatial convolution integrals. To solve this problem, we introduce the recursive convolution (RC) with vector fitting (VF) method to accelerate the computational speed. Through combining the diffraction nonlocal boundary with RC, we achieve the improved diffraction nonlocal BC. Then we propose a wide-angle three-dimensional parabolic equation (WA-3DPE) decomposition algorithm in which the improved diffraction nonlocal BC is applied and we utilize it to predict the wave propagation problems in the complex environment. Numeric computation and measurement results demonstrate the computational accuracy and speed of the WA-3DPE decomposition model with the improved diffraction nonlocal BC.

On the extrication of large objects from the ocean bottom (the breakout phenomenon)

1982 ◽  
Vol 117 ◽  
pp. 211-231 ◽  
Author(s):  
Mostafa A. Foda
Keyword(s):  
Boundary Layer ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Time Dependent ◽  
Ocean Bottom ◽  
Leading Order ◽  
Boundary Layer Approximation ◽  
Slender Bodies ◽  
Axisymmetric Bodies ◽  
Time Dependent Analysis

An analytical theory is developed to describe how negative pressure, (or ‘mud suction’, as it is sometimes referred to) develops underneath a body as it detaches itself from the ocean bottom. Biot's quasistatic equations of poro-elasticity are used to model the ocean bottom, and a general three-dimensional time-dependent analysis of the problem is worked out first using the boundary-layer approximation recently proposed by Mei and Foda. Then, explicit leading-order analytical solutions are presented for the problems of extrication of slender bodies as well as axisymmetric bodies from the ocean bottom.

Sign in / Sign up

Export Citation Format

Share Document