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Preliminary Concepts
Published in Hillel Rubin, Joseph Atkinson, Environmental Fluid Mechanics, 2001
Most finite difference methods induce some additional spreading, referred to as numerical diffusion or numerical dispersion. Since the present discussion refers to one-dimensional models, we will use the term dispersion, consistent with earlier discussion (Sec. 10.5). The total dispersion actually present in the solution of any finite difference method is the sum of the input dispersivity, Ein, and the numerical dispersion, EN, introduced by the numerical technique, i.e.,
Prediction of reflection including diffraction
Published in Trevor J. Cox, Peter D'Antonio, Acoustic Absorbers and Diffusers, 2016
Trevor J. Cox, Peter D'Antonio
When sound waves propagate in a non-dispersive medium such as air, their propagation velocity is isotropic and independent of frequency. In an FDTD simulation, however, the phase velocities of the propagated waves deviate from this ideal. This artefact, referred to as numerical dispersion,29 is rooted in the nature of finite difference approximations and is both frequency and direction dependent. In general, numerical dispersion becomes more dominant with increasing frequency and, as such, imposes a limitation on the usable bandwidth of the simulation.
Numerical wave dispersion considering linear and higher order finite elements
Published in G.N. Pande, S. Pietruszczak, H.F. Schweiger, Numerical Models in Geomechanics, 2020
For wave propagation problems, the estimation of wave velocity is affected by some error called numerical dispersion and depending on many parameters such as mesh refinement, time integration scheme, element type... The classical rule is to choose the element size between a tenth and a twentieth of the wavelength. It could not be sufficient to analyze far field wave propagation. For 2D-cases, the incidence has a strong influence on numerical dispersion.
A Mesh Grading Technique for Near-fault Seismic Wave Propagation in Large Velocity-contrast Viscoelastic Earth Media
Published in Journal of Earthquake Engineering, 2022
One approach is to use continuous nonuniform grid technique (Moczo 1989; Moczo et al. 1997; Pitarka 1999). The smaller grid spacing is used for the low-velocity region, and the larger grid spacing is used for the most part of high-velocity region except for the interface. It is clear that the grids in low-velocity and high-velocity regions have some shared nodes at the interface between them and the length of adjacent two shared nodes at the interface is determined by numerical dispersion relation of grids in low-velocity region. Then, the length of grid sides at the interface must be small enough. It means that there always exits small spacing steps in high-velocity region. To meet stability requirement in high-velocity region, a small time step size needs to be used. This will surely result in temporal oversampling in the low-velocity region.
A 3-D fourth-order one-step leapfrog HIE-FDTD method with CPML
Published in International Journal of Electronics, 2021
Mian Dong, Juan Chen, Xiaodan Zhang, Anxue Zhang
Figures 1 and 2 show the normalised phase error calculated by using the proposed method. For comparison, the normalised phase error calculated by using the traditional FDTD method and the traditional HIE-FDTD method are also plotted in these figures. The numerical dispersion relation of the traditional FDTD method and the traditional HIE-FDTD method are given, respectively, as follows,
Linear Stability of the Activation-Energy-Asymptotics Reactive-Layer Structure: I. Liñán’s Premixed-Flame Regime
Published in Combustion Science and Technology, 2023
which recovers the result previously obtained by Kim (1998). In Figure 1, the asymptotic dispersion relation (40) exhibits a satisfactory agreement with the numerical dispersion relation, particularly as . However, it must be noted that the above asymptotic dispersion relation is valid only for .