Extrapolation non-reflecting boundary conditions

Liao, Zhenpeng

doi:10.1016/0165-2125(96)00010-8

Cited by 73 publications

(36 citation statements)

References 20 publications

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“…Among the ABC, there is another method not mentioned in the text, which is called Liao's ABC (Liao et al, 1984;Liao, 1996). Liao's ABC extrapolates wave equations in the time and space domain based on the Newton's backward differential.…”

Section: Discussionmentioning

confidence: 99%

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Gao

Song

Zhang

et al. 2017

Exploration Geophysics

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Abstract. Absorbing boundary conditions are necessary in numerical simulation for reducing the artificial reflections from model boundaries. In this paper, we overview the most important and typical absorbing boundary conditions developed throughout history. We first derive the wave equations of similar methods in unified forms; then, we compare their absorbing performance via theoretical analyses and numerical experiments. The Higdon boundary condition is shown to be the best one among the three main absorbing boundary conditions that are based on a one-way wave equation. The Clayton and Engquist boundary is a special case of the Higdon boundary but has difficulty in dealing with the corner points in implementaion. The Reynolds boundary does not have this problem but its absorbing performance is the poorest among these three methods. The sponge boundary has difficulties in determining the optimal parameters in advance and too many layers are required to achieve a good enough absorbing performance. The hybrid absorbing boundary condition (hybrid ABC) has a better absorbing performance than the Higdon boundary does; however, it is still less efficient for absorbing nearly grazing waves since it is based on the one-way wave equation. In contrast, the perfectly matched layer (PML) can perform much better using a few layers. For example, the 10-layer PML would perform well for absorbing most reflected waves except the nearly grazing incident waves. The 20-layer PML is suggested for most practical applications. For nearly grazing incident waves, convolutional PML shows superiority over the PML when the source is close to the boundary for large-scale models. The Higdon boundary and hybrid ABC are preferred when the computational cost is high and high-level absorbing performance is not required, such as migration and migration velocity analyses, since they are not as sensitive to the amplitude errors as the full waveform inversion.

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Section: Discussionmentioning

confidence: 99%

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Gao

Song

Zhang

et al. 2017

Exploration Geophysics

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“…The artificial boundaries, such as transmitting boundary [17], Clayton-Engquist boundary [18,19], viscous boundary [20,21], and viscous-spring boundary [22,23], are proposed to eliminate reflection and to simulate the process of wave transmission. The transmitting boundary has high accuracy, but a certain amount of nodes and elements should be added on the boundary that needs large computing storage capacity.…”

Section: Seismic Wave Input Methodsmentioning

confidence: 99%

Oblique Incidence of Seismic Wave Reflecting Two Components of Design Ground Motion

Cen

et al. 2018

Shock and Vibration

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The wave field on the artificial boundary was separated into the free field without local topography effect and scattering field induced by local topography effect. The simulation of the free field under obliquely incident waves was conducted. Based on the assumption that the components of design ground motion were treated as the coincidence of oblique P wave and oblique SV wave, the relationship between the oblique input waves and the design ground motion was established in the free field. Further, the contributions to the two components of design ground motion of obliquely incident waves were discussed. The calculation model in time domain was achieved by the combination of the propagation characteristics of obliquely incident waves and the artificial boundary in the free field. The seismic response to the design ground motion was produced on the free surface. The verification of the 2D half-space model under oblique input waves indicated that the wave input method can accurately reflect the design ground motion on the free surface. Application of an earth-rock dam showed that oblique incidence of seismic waves results in significantly different dynamic response compared with the normal incidence. The proposed method can also be employed in the seismic analysis of large span structures with nonuniform ground motion input.

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“…The MTF for the non-reflecting boundary conditions was first proposed by Liao [10], via a direct simulation of one way wave propagation using a space-time extrapolation by an artificial wave speed. According to the theory of Liao, for the N-order MTF, the velocity potential on the open boundary can be written as where C n j is the binominal coefficients The Sommerfeld's radiation condition [13] is known as follows:…”

Section: Open Boundary Conditionmentioning

confidence: 99%

“…The Sommerfeld-Orlanski's condition have been widely used by researchers [6,7], but it cannot give a good result for irregular waves simulation. Marching with linear solutions method is used by Liu [10,11], but the computation cost is huge. The piston-like active wave absorber is also used in common [2,3], but it is hard to be applied in 3D problems.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Irregular Waves in a Numerical Wave Tank

Yuyun²,

HuiLonga

et al. 2015

Polish Maritime Research

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The time domain boundary element method was utilized to simulate the propagation of the irregular waves in a numerical wave tank. The problem was solved in a time-marching scheme, upon the irregular waves being fed through the inflow boundary, in which the theoretical solution was obtained from the wave energy spectrum. The open boundary condition was modeled by the multi transmitting formula (MTF), in which the phase velocity was calculated according to the Sommerfeld's condition. The velocity potential and wave elevation were directly obtained by integrating the free surface condition twice, with respect to time. The accuracy of the developed numerical scheme was verified by simulating the propagation of irregular waves. The numerical results show good agreements with the analytical solutions, which prove that the proposed scheme is a promising way to the simulation of wave-body interactions.

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Extrapolation non-reflecting boundary conditions

Cited by 73 publications

References 20 publications

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Oblique Incidence of Seismic Wave Reflecting Two Components of Design Ground Motion

Simulation of Irregular Waves in a Numerical Wave Tank

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