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R. A. C. Germanos, L. F. De Souza
2018 Revista de Engenharia Térmica  
Four different space discretization schemes are tested, namely, a second order finite-differences, a fourth order finitedifferences, a fourth order finite-differences compact scheme and a sixth order finite-differences  ...  The results confirm that high order accuracy schemes can be more efficient for simulation of acoustic waves, especially the waves with high frequency.  ...  The discretization error was analyzed and tested for different space discretization schemes, namely, a second order finite-differences, a fourth order finite-differences, a fourth order finite-differences  ... 
doi:10.5380/reterm.v5i1.61663 fatcat:dmyjy7ywqbhure6k7vxn5gkbne

Low-Dissipation and Low-Dispersion Runge–Kutta Schemes for Computational Acoustics

F.Q. Hu, M.Y. Hussaini, J.L. Manthey
1996 Journal of Computational Physics  
are the classical third-and fourth-order Rungeand dispersion errors.  ...  The used in wave propagation problems using high-order spaproposed LDDRK schemes are remarkably more efficient than the classical Runge-Kutta schemes for acoustic computations.  ...  In [12] , an Adams-Bashforth-For simplicity of discussion, we consider the convective type multistep time integration scheme was optimized wave equation for acoustic calculations.  ... 
doi:10.1006/jcph.1996.0052 fatcat:szf345uspjcx5ljh45zf7sr75e

Fourth‐order finite‐differenceP-SVseismograms

Alan R. Levander
1988 Geophysics  
Fourth-order Finite-difference P-W seismograms 1427  ...  I describe the properties of a fourth-order accurate space, second-order accurate time two-dimensional P-Sk' finite-difference scheme based on the Madariaga-Virieux staggered-grid formulation.  ...  ACKNOWLEDGMENTS I would like to thank the Chevron Oil Field Research Laboratory for supporting development of the finite-difference scheme.  ... 
doi:10.1190/1.1442422 fatcat:lfuuruhntrdopaqdmxilai4bvq

An optimized staggered variable-grid finite-difference scheme and its application in cross-well acoustic survey

HaiBo Zhao, XiuMing Wang
2008 Science Bulletin  
In this paper, an optimized staggered variable-grid finite-difference (FD) method is developed in velocity-stress elastic wave equations.  ...  On the basis of the dispersion-relation-preserving (DRP), a fourth-order finite-difference operator on non-uniform grids is constructed. The proposed algorithm is a continuous variable-grid method.  ...  In order to improve computation efficiency of the FD scheme, based on the local parameters, the most efficient grid layout can be obtained by assembling grids with different spacing that cover different  ... 
doi:10.1007/s11434-008-0042-x fatcat:jcmsmkmwojbxbp2ufton7hvoaa

Second-order Scalar Wave Field Modeling with First-order Perfectly Matched Layer

Xiaoyu Zhang, Dong Zhang, Qiong Chen, Yan Yang
2018 Solid Earth Discussions  
finite-difference algorithm based on the second-order wave equation.  ...  The finite-difference algorithm in the form of a second-order wave equation is one of the commonly used forward numerical algorithms.  ...  Numeric modeling of Eq. (1) is expressed as follows. 20 2. 1 201 Conventional-grid finite-difference scheme21The discretization of the acoustic wave equation (1) with a 2M-order finite-difference scheme  ... 
doi:10.5194/se-2018-48 fatcat:usfyldlwzvfa7e7maxu6qd6jja

Time Domain Room Acoustic Solver with Fourth-Order Explicit FEM Using Modified Time Integration

Takumi Yoshida, Takeshi Okuzono, Kimihiro Sakagami
2020 Applied Sciences  
Earlier, the authors proposed an efficient room acoustic solver using explicit TD-FEM having fourth-order accuracy in both space and time using low-order discretization techniques.  ...  This paper presents a proposal of a time domain room acoustic solver using novel fourth-order accurate explicit time domain finite element method (TD-FEM), with demonstration of its applicability for practical  ...  This conventional dispersion-reduced explicit TD-FEM is computationally efficient by virtue of its use of linear elements and low-order finite difference approximation in time.  ... 
doi:10.3390/app10113750 fatcat:xmpikgrn2vbffpio3qdnieddca


2001 International Conference on Aerospace Sciences and Aviation Technology  
Computations are performed using 3-point fourth-order compact implicit McCormick-type scheme to approximate the spatial derivatives and the two steps 5-6 alternating 2-N storage Low-Dispersion and -Dissipation  ...  Runge-Kutta (LDDRK) method as a time marching scheme.  ...  5-6, 2-N storage Low-Dispersion and -Dissipation Runge-Kutta method (LDDRK) as a time marching scheme.  ... 
doi:10.21608/asat.2001.59778 fatcat:z7cv3kh4rbb3bkai3d3mnoeqp4

Elimination of numerical dispersion in finite‐difference modeling and migration by flux‐corrected transport

Tong Fei, Ken Larner
1995 Geophysics  
However, conventional finite-difference methods for solving the acousticwave equation suffer from numerical dispersion when too few samples per wavelength are used.  ...  ABSTRACT Finite-difference acoustic-wave modeling and reverse-time depth migration based on the full wave equation are general approaches that can take into account arbitary variatious in velocity and  ...  This wave equation for inhomogencous media can be approximated by an explicit, conventional finite-difference scheme.  ... 
doi:10.1190/1.1443915 fatcat:krtakpuwifgfxgqbbrdvf6ragu

An efficient Helmholtz solver for acoustic transversely isotropic media

Zedong Wu, Tariq Alkhalifah
2017 Geophysics  
Since only one equation is required to obtain a 69 numerical solution, the new proposed scheme is more efficient than conventional schemes 70 that solve a system of second-order differential equations.  ...  Finally, we iteratively solve the 18 simpler lower-order elliptical wave equation for a modified source function that includes 19 the non-elliptical terms represented in the Fourier domain.  ...  of second-order differential equations, and 32 proposed a computationally efficient scheme.  ... 
doi:10.1190/geo2017-0618.1 fatcat:j7x43v5tuvcxfhsndo2tgjfnt4

Numerical analysis of the lattice Boltzmann method for simulation of linear acoustic waves

Dattaraj B. Dhuri, Shravan M. Hanasoge, Prasad Perlekar, Johan O. A. Robertsson
2017 Physical review. E  
Our results show that the LB scheme performance is comparable to the classical second-order finite-difference schemes.  ...  Given its efficiency for parallel computation, the LB method can be a cost effective tool for the simulation of linear acoustic waves in complex geometries and multiphase media.  ...  Blanch for useful conversations. We thank the anonymous reviewers for their valuable comments and suggestions.  ... 
doi:10.1103/physreve.95.043306 pmid:28505847 fatcat:bgsyectnmzc7dlqfu7birp4d2m

An Efficiently Parallelized High-Order Aeroacoustics Solver Using a Characteristic-Based Multi-Block Interface Treatment and Optimized Compact Finite Differencing

Bidur Khanal, Alistair Saddington, Kevin Knowles
2017 Aerospace (Basel)  
This paper presents the development of a fourth-order finite difference computational aeroacoustics solver.  ...  Both explicit and implicit finite difference spatial discretization schemes are widely used [3] [4] [5] .  ...  Specifically, a fourth-order pentadiagonal type of central compact finite-difference scheme in space and fourth-order explicit temporal differencing are used to minimise the dissipation and dispersion  ... 
doi:10.3390/aerospace4020029 fatcat:wcivlqnw5rcvrfdgtbv7lpthhy

A modified Lax-Wendroff correction for wave propagation in media described by Zener elements

J. O Blanch, J. O. A. Robertsson
1997 Geophysical Journal International  
S U M M A R Y A modified Lax-Wendroff correction for wave propagation in attenuating and dispersive media described by Zener elements is presented.  ...  The technique may be applied to a wide variety of hyperbolic problems. Here, the concept is illustrated for wave propagation in visco-acoustic media.  ...  Bergmann for valuable discussions and support. ETH-Geophysics Contr. No. 928. This research was partially supported by FOA grant E6011.  ... 
doi:10.1111/j.1365-246x.1997.tb01229.x fatcat:lip3u2z3sffxdbbq53dtjtk6yi

Numerical anisotropy in finite differencing

Adrian Sescu
2015 Advances in Difference Equations  
Then, several important studies that were focused on optimizations of finite difference schemes with the objective of reducing the numerical anisotropy are discussed.  ...  A commonly used term for the aforementioned multidimensional discretization error is the numerical anisotropy or isotropy error.  ...  Acknowledgements The author would like to thank Ray Hixon, Abdollah Afjeh, Vasanth Allampalli, Shivaji Medida, Daniel Ingraham, and Carmen Sescu for constructive support and encouragement.  ... 
doi:10.1186/s13662-014-0343-0 fatcat:57a5athkbfegfc26objvixgjdm

Grid dispersion and stability criteria of some common finite-element methods for acoustic and elastic wave equations

Jonás D. De Basabe, Mrinal K. Sen
2007 Geophysics  
New results can be compared with grid-dispersion results of some classical finite-difference methods ͑FDM͒ used for acoustic or elastic wave propagation.  ...  The staggered-grid FDM is an efficient scheme, but the dispersion is angle dependent with larger values along the grid axes.  ...  This work was done while Jonas De Basabe was supported by a Ph.D. fellowship from the Mexican National Council for Science and Technology ͑CONACYT͒.  ... 
doi:10.1190/1.2785046 fatcat:mtyc4opxofe4pku3fygkoygv3a

Second-order scalar wave field modeling with a first-order perfectly matched layer

Xiaoyu Zhang, Dong Zhang, Qiong Chen, Yan Yang
2018 Solid Earth  
finite-difference algorithm based on the second-order wave equation.  ...  The finite-difference algorithm in the form of a second-order wave equation is one of the commonly used forward numerical algorithms.  ...  High-order finite-difference schemes are able to control this numerical dispersion using a larger grid spacing compared with low-order schemes (Tan and Huang, 2014) .  ... 
doi:10.5194/se-9-1277-2018 fatcat:o3juuf4osvghtcaqwndqpdzqae
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