Study on Applicability of MacCormack Finite Difference Scheme in Generalized Coordinate System for Open Channel Flows.

In this paper, we consider the following problems: The existence of solution the stability of finite difference scheme and the non-negative property of numerical solution

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Analysis of Seismic Wavefield Characteristics in 3D Tunnel Models Based on the 3D Staggered-Grid Finite-Difference Scheme in the Cylindrical Coordinate System

Applied Sciences ◽

10.3390/app11135854 ◽

2021 ◽

Vol 11 (13) ◽

pp. 5854

Author(s):

Zhiwu Zuo ◽

Duo Li ◽

Pengfei Zhou ◽

Chunjin Lin ◽

Zhichao Yang ◽

...

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Coordinate System ◽

Finite Difference Scheme ◽

Forward Modeling ◽

Cylindrical Coordinate System ◽

Staggered Grid ◽

Geological Conditions ◽

Cylindrical Coordinate ◽

Seismic Wavefield

The accurate prediction of the geological conditions ahead of a tunnel plays an important role in tunnel construction. Among all forward geological prospecting methods, the seismic detection method is widely applied. However, due to the characteristics of the tunnel and the complexity of the geological conditions, the seismic wavefield is complicated. Carrying out a more realistic forward modeling method is vital for fully understanding the law of seismic wave propagation and the characteristics of seismic wavefield in the tunnel. In this paper, the 3D staggered-grid finite-difference scheme in the cylindrical coordinate system based on the decoupled nonconversion elastic wave equation is used to carry out the numerical simulation. This method can avoid the diffraction interferences produced at the edges of the tunnel face in the Cartesian coordinate system. Based on this forward modeling method, the characteristics of wavefield and propagation laws of seismic waves under three kinds of common typical unfavorable geological models were explored, which can provide theoretical guidance to seismic data interpretation of tunnel seismic forward prospecting in practice.

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Numerical analysis of unsteady open channel flows by means of moving boundary fitted coordinate system.

Doboku Gakkai Ronbunshu ◽

10.2208/jscej.1996.533_267 ◽

1996 ◽

pp. 267-272 ◽

Cited By ~ 2

Author(s):

Takashi Hosoda ◽

Nobuhisa Nagata ◽

Yoshio Muramoto

Keyword(s):

Numerical Analysis ◽

Coordinate System ◽

Open Channel ◽

Moving Boundary ◽

Channel Flows ◽

Open Channel Flows

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Domain-limited solution of the wave equation in Riemannian coordinates

Geophysics ◽

10.1190/geo2012-0027.1 ◽

2013 ◽

Vol 78 (1) ◽

pp. T21-T27 ◽

Cited By ~ 2

Author(s):

Adel Khalil ◽

Mohamed Hesham ◽

Mohamed El-Beltagy

Keyword(s):

Wave Equation ◽

Finite Difference ◽

Difference Scheme ◽

Coordinate System ◽

Finite Difference Scheme ◽

Reverse Time ◽

Time Step ◽

Velocity Models ◽

Time Migration ◽

Computational Performance

We propose to solve the two-way time domain acoustic wave equation in a generalized Riemannian coordinate system via finite-differences. The coordinate system is defined in such a way that one of its independent variables conforms to the primary wavefront, for example, using a ray coordinate system with the traveltime being one of the coordinates. At each finite-difference time-step, the solution domain is limited to a narrow corridor around the primary wavefront, leading to an increase in the computational performance. A new finite-difference scheme is introduced to stabilize the solution and facilitate its implementation. This new scheme is a blend of the simple explicit and the stable implicit schemes. As a proof of concept, the proposed method is compared to the classical explicit finite-difference scheme performed in Cartesian coordinates on two synthetic velocity models with varying complexities. At a reduced cost, the proposed method produces similar results to the classical one; however, some amplitude differences arise due to various implementation issues. The most direct application for the proposed method is the source side of reverse time migration.

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