Composite absorbing boundaries for the numerical simulation of seismic waves

1994 ◽  
Vol 84 (1) ◽  
pp. 185-191
Author(s):  
Nanxun Dai ◽  
Antonios Vafidis ◽  
Ernest Kanasewich
Keyword(s):  
Numerical Simulation ◽  
Transition Zone ◽  
Seismic Waves ◽  
Absorbing Boundary Conditions ◽  
The Body ◽  
Body Waves ◽  
Filter Method ◽  
Characteristic Analysis ◽  
Absorbing Boundary ◽  
The One

Abstract Composite absorbing boundary methods are developed for the numerical simulation of seismic waves. These methods combine low-angle absorbing boundary conditions, based on the characteristic analysis of one-dimensional wave equations, with either of two novel wave field modification approaches, namely the anisotropic filters and the one-way sponge filters. The anisotropic filter method adjusts the propagation direction of the waves, so that they reach the boundary at normal angles. The one-way sponge filter method endows the transition zone with a dissipation mechanism that selectively damps the incoming waves. These methods absorb not only the body waves but also the surface waves. A narrow transition zone adjacent to a computational boundary is introduced whose width is smaller than in the sponge filter approach. Numerical examples illustrate the effectiveness of these methods in absorbing the artificial reflections.

Statement of absorbing Mur boundary conditions of the first order of accuracy for solving problems of electrodynamics by the method of finite differences in the time domain

2021 ◽  
Vol 8 ◽  
pp. 57-68
Author(s):  
R.Yu. Borodulin ◽  
N.O. Lukyanov
Keyword(s):  
Boundary Conditions ◽  
Time Domain ◽  
Correct Choice ◽  
Absorbing Boundary Conditions ◽  
Practical Significance ◽  
Stable Operation ◽  
Absorbing Boundary ◽  
Spherical Waves ◽  
The One ◽  
The Time Domain

Problem statement. The accuracy and convergence of calculations for solving problems of electrodynamics by the finite difference method in the time domain significantly depends on the correct choice of parameters and the correct setting of the absorbing boundary conditions (ABC). Two main types of absorbing boundary conditions are known: Mur ABC; Beranger ABC. It is believed that the Mur ABC is less effective at absorbing spherical waves than the Beranger ABC, but they do not require the introduction of additional parameters (the so-called "Beranger fields"), which simplifies the implementation of program code and saves computer RAM. Calculations have shown that the efficiency of the Mur ABC will depend on their thickness. On the one hand, an increase in the thickness of the ABC layers will lead to an increase in the accuracy of calculations, on the other hand, to an increase in the size of the calculation area and, as a result, an increase in RAM. The problem arises of determining the criterion for evaluating the efficiency of ABC to determine their optimal thickness. Goal. Identification of new factors that make it possible to use the Mur ABC as efficiently as the Beranger ABC, while significantly saving computer resources. Result. The expressions for the ABC are presented, taking into account the interaction of all components of the electromagnetic field within a single cell of the FDTD. Calculations of the reflection coefficient – a criterion for evaluating the efficiency of the ABC, are presented. Practical significance. Calculations are presented that allow automating the selection of ABC parameters for their stable operation in solving electrodynamic problems.

scholarly journals Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities

2011 ◽  
Vol 10 (5) ◽  
pp. 1280-1304 ◽  
Author(s):  
Pauline Klein ◽  
Xavier Antoine ◽  
Christophe Besse ◽  
Matthias Ehrhardt
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Absorbing Boundary Conditions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Absorbing Boundary ◽  
One Dimensional ◽  
Nonlinear Potential ◽  
Linear And Nonlinear ◽  
The One

AbstractWe propose a hierarchy of novel absorbing boundary conditions for the one-dimensional stationary Schrödinger equation with general (linear and nonlinear) potential. The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schrödinger equations. It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition. Finally, we give the extension of these ABCs to N-dimensional stationary Schrödinger equations.

Wave Equation Simulation by Finite-Element Method with Perfectly Matched Layer

2012 ◽  
Vol 524-527 ◽  
pp. 96-100 ◽  
Author(s):  
Hong Wei Guo ◽  
Shang Xu Wang ◽  
Nai Chuan Guo ◽  
Wei Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Conditions ◽  
Absorption Effect ◽  
Absorbing Boundary ◽  
The One ◽  
First Time ◽  
Element Method

In numerical simulation, the treatment of boundary conditions is of great significance. In this paper, we have deduced the one order governing equations of the acoustic wave finite-element method with perfectly matched layer (PML) for the first time. The one order equations are easier to realize than the two order form and have a good absorption effect. Then, we have analyzed the absorption effect of the absorbing boundary conditions (ABCs) and the PML. Finally, we get some useful conclusions.

Characteristic Analysis of the Transition Zone in Carbon Dioxide Miscible Flooding

2013 ◽  
Vol 734-737 ◽  
pp. 497-501
Author(s):  
Chang Lin Liao ◽  
Xin Wei Liao ◽  
Ju Li ◽  
Ning Lu
Keyword(s):  
Carbon Dioxide ◽  
Numerical Simulation ◽  
Interfacial Tension ◽  
Laboratory Experiment ◽  
Transition Zone ◽  
Zone Size ◽  
Characteristic Analysis ◽  
Injection Volume ◽  
Miscible Flooding ◽  
Carbon Dioxide Miscible Flooding

Study on the characteristic of the transition zone in CO2-oil system has important meaning for the research of CO2 miscible flooding. In this paper, one of crude oil samples in Xinjiang oilfield was taken as an example. The minimum miscible pressure (MMP) of CO2-oil system was confirmed through laboratory experiment and numerical simulation separately. And the characteristic of the transition zone was analyzed. The transition zone size and interfacial tension in miscible process were quantified. And their variation tendencies along with the change of the pressure and CO2 injection volume were studied. The results show that it is easier to reach miscible state in higher pressure and CO2 injection volume. This work provides a reference for the further research of CO2 miscible flooding.

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