Numerical dispersion of finite difference method

2006 ◽  
Vol 120 (5) ◽  
pp. 3364-3364
Author(s):  
Yoshimitsu Takasawa
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Dispersion

scholarly journals VISCO-ACOUSTIC MODELING IN THE FREQUENCY DOMAIN USING A MIXED-GRID FINITE-DIFFERENCE METHOD AND ATTENUATION-DISPERSION MODEL

2019 ◽  
Vol 37 (2) ◽  
Author(s):  
S.K. Avendaño ◽  
M.A. Ospina ◽  
J.C. Muñoz-Cuartas ◽  
H. Montegranario
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Frequency Domain ◽  
Difference Method ◽  
Seismic Attenuation ◽  
Numerical Dispersion ◽  
Acoustic Medium ◽  
Time Migration ◽  
Point Scheme

ABSTRACT. Seismic modeling is an important step in the process used for imaging Earth sub-surface. Current applications require accurate models associated with solutions of the equation of wave propagation in realistic medium. In this work, we propose a modeling for 2D wave propagation in a visco-acoustic medium with variable velocity and density, handled in the frequency domain under conditions that describe dissipation depending on the quality factor Q. We use mixed-grid finite-difference method and optimize it for the case of the visco-acoustic medium with the aim to minimize numerical dispersion. We present solutions for test cases in homogeneous media and compare the analytic solutions. Further, we compare the solution using conventional grid (5-point scheme) and our mixed grid implementation (9-point scheme), finding a better response with the mixed grid 9-point scheme. We also studied the characteristics of the numerical solution, wave fields for P-waves are discussed for different velocity profiles, damping functions and Q values finding that the method performs very well with potential in applications that require full knowledge of the wave field such as Full Waveform Inversion or Reverse Time Migration. Keywords: seismic attenuation, wave propagation modeling, visco-acoustic medium, quality factor.RESUMO. A modelagem sísmica é um passo importante no processo da construção de imagens da sub-superfície da Terra. Aplicações atuais exigem modelos de exatidão associados a soluções da equação de propagação de ondas em meio realista. Neste trabalho, nós propomos uma modelagem para propagação de ondas 2D em um meio visco-acústico com velocidade e densidade variáveis, manipuladas no domínio da frequência sob condições que descrevem a dissipação dependendo do fator de qualidade Q. Utilizamos o método de diferenças finitas em redes mistas e otimizamos para o caso do meio visco-acústico com o objetivo de minimizar a dispersão numérica. Apresentamos soluções para casos de teste em meios homogêneos e comparamos com as soluções analíticas. Além disso, comparamos a solução usando uma rede convencional (5-pontos) e nossa implementação de redes mistas (9-pontos), encontrando uma melhor resposta com o esquema de 9-pontos da rede mista. Também estudamos as características da solução numérica, campos de onda para ondas P são discutidos para diferentes perfis de velocidade, funções de amortecimento e valores de Q, descobrindo que o método funciona muito bem com potencial em aplicações que exigem conhecimento completo do campo de onda, como inversão de forma de onda completa ou Migração de Tempo Inverso.Palavras-chave: atenuação sísimica, modelagem de propagação de onda, meio visco-acústico, fator de qualidade.

M-Adaptation in the mimetic finite difference method

2014 ◽  
Vol 24 (08) ◽  
pp. 1621-1663 ◽  
Author(s):  
Vitaliy Gyrya ◽  
Konstantin Lipnikov ◽  
Gianmarco Manzini ◽  
Daniil Svyatskiy
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Dispersion ◽  
Maximum Principles ◽  
The Family ◽  
Mimetic Finite Difference Method ◽  
Primal And Dual ◽  
Dual Forms ◽  
Equivalent Properties

The mimetic finite difference method produces a family of schemes with equivalent properties such as the stencil size, stability region, and convergence order. Each member of this family is defined by a set of parameters which can be chosen locally for every mesh element. The number of parameters depends on the geometry of a particular mesh element. M-Adaptation is a new adaptation methodology that identifies a member of this family with additional (superior) properties compared to the other schemes in the family. We analyze the enforcement of the discrete maximum principles for the diffusion equation in the primal and dual forms, the reduction of numerical dispersion and anisotropy for the acoustic wave equation, and the optimization of the performance of multi-grid solvers.

Staggered-Grid Finite Difference Method for Numerical Simulation of the Formulated BISQ Model

2013 ◽  
Vol 756-759 ◽  
pp. 4742-4746
Author(s):  
Xin Ming Zhang ◽  
Chang Ming Fu ◽  
Ting Ting Guo
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Layer Method ◽  
Bisq Model ◽  
Flux Corrected Transport ◽  
Transport Method

In this paper, based on the formulated BISQ model including the Biot-flow and squirt-flow mechanism simultaneously, the elastic wave propagation in the isotropic porous medium filled with fluids is simulated by the staggered grid finite difference method. The perfectly matched layer method and the flux-corrected transport method are used to eliminate the effect of boundary reflection and numerical dispersion effect. The results of numerical simulation demonstrate that the method is effective.

HEAT TRANSFER IN LARGE RUBBER ELEMENTS THROUGH OF MODELING BY FINITE DIFFERENCE METHOD

2019 ◽  
Author(s):  
Lucas Peixoto ◽  
Ane Lis Marocki ◽  
Celso Vieira Junior ◽  
Viviana Mariani
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method

Weighted Finite Difference and Boundary Element Methods Applied to Groundwater Pollution Problems

1991 ◽  
Vol 23 (1-3) ◽  
pp. 517-524
Author(s):  
M. Kanoh ◽  
T. Kuroki ◽  
K. Fujino ◽  
T. Ueda
Keyword(s):  
Boundary Element Method ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Element ◽  
Difference Method ◽  
Groundwater Pollution ◽  
Small Region ◽  
Boundary Element Methods ◽  
Computational Time ◽  
Element Method

The purpose of the paper is to apply two methods to groundwater pollution in porous media. The methods are the weighted finite difference method and the boundary element method, which were proposed or developed by Kanoh et al. (1986,1988) for advective diffusion problems. Numerical modeling of groundwater pollution is also investigated in this paper. By subdividing the domain into subdomains, the nonlinearity is localized to a small region. Computational time for groundwater pollution problems can be saved by the boundary element method; accurate numerical results can be obtained by the weighted finite difference method. The computational solutions to the problem of seawater intrusion into coastal aquifers are compared with experimental results.

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