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Pseudo-spectral Method (pseudo-spectral + method)

Distribution by Scientific Domains

Engineering	83%

Selected Abstracts

Regional tomographic inversion of the amplitude and phase of Rayleigh waves with 2-D sensitivity kernels

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2006
Yingjie Yang
SUMMARY In this study, we test the adequacy of 2-D sensitivity kernels for fundamental-mode Rayleigh waves based on the single-scattering (Born) approximation to account for the effects of heterogeneous structure on the wavefield in a regional surface wave study. The calculated phase and amplitude data using the 2-D sensitivity kernels are compared to phase and amplitude data obtained from seismic waveforms synthesized by the pseudo-spectral method for plane Rayleigh waves propagating through heterogeneous structure. We find that the kernels can accurately predict the perturbation of the wavefield even when the size of anomaly is larger than one wavelength. The only exception is a systematic bias in the amplitude within the anomaly itself due to a site response. An inversion method of surface wave tomography based on the sensitivity kernels is developed and applied to synthesized data obtained from a numerical simulation modelling Rayleigh wave propagation over checkerboard structure. By comparing recovered images to input structure, we illustrate that the method can almost completely recover anomalies within an array of stations when the size of the anomalies is larger than or close to one wavelength of the surface waves. Surface wave amplitude contains important information about Earth structure and should be inverted together with phase data in surface wave tomography. [source]

An efficient domain-decomposition pseudo-spectral method for solving elliptic differential equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2008
N. Mai-Duy
Abstract In this paper, a new numerical scheme based on non-overlapping domain decompositions and integrated Chebyshev approximations for solving elliptic differential equations (DEs) is presented. The distinguishing feature of the present scheme is that it achieves a Cp continuous solution across the interfaces (p is the order of the DE). Several test problems are employed to verify the method. The obtained results indicate that the achievement of higher-order smoothness leads to a significant improvement in accuracy. Copyright © 2007 John Wiley & Sons, Ltd. [source]

A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2003
K. Djidjeli
Abstract An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. =10pt An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable. The method is second order in time and all-order in space. The method presented here is for the RLW equation and its generalized form, but it can be implemented to a broad class of non-linear long wave equations (Equation (2)), with obvious changes in the various formulae. Test problems, including the simulation of a single soliton and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. Copyright © 2003 John Wiley & Sons, Ltd. [source]

An explicit formulation for the evolution of nonlinear surface waves interacting with a submerged body

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007
Christopher P. Kent
Abstract An explicit formulation to study nonlinear waves interacting with a submerged body in an ideal fluid of infinite depth is presented. The formulation allows one to decompose the nonlinear wave,body interaction problem into body and free-surface problems. After the decomposition, the body problem satisfies a modified body boundary condition in an unbounded fluid domain, while the free-surface problem satisfies modified nonlinear free-surface boundary conditions. It is then shown that the nonlinear free-surface problem can be further reduced to a closed system of two nonlinear evolution equations expanded in infinite series for the free-surface elevation and the velocity potential at the free surface. For numerical experiments, the body problem is solved using a distribution of singularities along the body surface and the system of evolution equations, truncated at third order in wave steepness, is then solved using a pseudo-spectral method based on the fast Fourier transform. A circular cylinder translating steadily near the free surface is considered and it is found that our numerical solutions show excellent agreement with the fully nonlinear solution using a boundary integral method. We further validate our solutions for a submerged circular cylinder oscillating vertically or fixed under incoming nonlinear waves with other analytical and numerical results. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Highly accurate solutions of the bifurcation structure of mixed-convection heat transfer using spectral method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2002
M. Selmi
Abstract This paper is concerned with producing highly accurate solution and bifurcation structure using the pseudo-spectral method for the two-dimensional pressure-driven flow through a horizontal duct of a square cross-section that is heated by a uniform flux in the axial direction with a uniform temperature on the periphery. Two approaches are presented. In one approach, the streamwise vorticity, streamwise momentum and energy equations are solved for the stream function, axial velocity, and temperature. In the second approach, the streamwise vorticity and a combination of the energy and momentum equations are solved for stream function and temperature only. While the second approach solves less number of equations than the first approach, a grid sensitivity analysis has shown no distinct advantage of one method over the other. The overall solution structure composed of two symmetric and four asymmetric branches in the range of Grashof number (Gr) of 0,2 × 106 for a Prandtl number (Pr) of 0.73 has been computed using the first approach. The computed structure is comparable to that found by Nandakumar and Weinitschke (1991) using a finite difference scheme for Grashof numbers in the range of 0,1×106. The stability properties of some solution branches; however, are different. In particular, the two-cell structure of the isolated symmetric branch that has been found to be unstable by the study of Nandakumar and Weinitschke is found to be stable by the current study. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Instabilities and bifurcations in lid-driven cavity flows

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Hendrik C. Kuhlmann Dr.
The three-dimensional flow of an incompressible Newtonian fluid in a rectangular slab is calculated numerically using a pseudo-spectral method. The fluid motion is driven by two facing sidewalls which can move in parallel or anti-parallel directions. Examples for bifurcations from two-dimensional to three-dimensional flows are given for spanwise periodic systems. For a comparison with previous experimental results rigid end walls are also considered. Differences between periodic and rigid end conditions are highlighted. [source]