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Wave Problems (wave + problem)

Distribution by Scientific Domains

Engineering	80%

Selected Abstracts

Comparison of three second-order accurate reconstruction schemes for 2D Euler and Navier,Stokes compressible flows on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2001
N. P. C. Marques
Abstract This paper reports an intercomparison of three second-order accurate reconstruction schemes to predict 2D steady-state compressible Euler and Navier,Stokes flows on unstructured meshes. The schemes comprise one monotone slope limiter (Barth and Jespersen, A1AA Paper 89-0366, 1989) and two approximately monotone methods: the slope limiter due to Venkatakrishnan and a data-dependent weighting least-squares procedure (Gooch, Journal of Computational Physics, 1997; 133:6,17). In addition to the 1D scalar wave problem, comparisons were performed under two inviscid test cases: a supersonic 10° ramp and a supersonic bump; and two viscous laminar compressible flow cases: the Blasius boundary layer and a double-throated nozzle. The data-dependent oscillatory behaviour is found to be dependent on a user-supplied constant. The three schemes are compared in terms of accuracy and computational efficiency. The results show that the data-dependent procedure always returns a numerical steady-state solution, more accurate than the ones returned by the slope limiters. Its use for Navier,Stokes flow calculations is recommended. Copyright © 2001 John Wiley & Sons, Ltd. [source]

A numerical scheme for strong blast wave driven by explosion

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2006
Kaori Kato
Abstract After the detonation of a solid high explosive, the material has extremely high pressure keeping the solid density and expands rapidly driving strong shock wave. In order to simulate this blast wave, a stable and accurate numerical scheme is required due to large density and pressure changes in time and space. The compressible fluid equations are solved by a fractional step procedure which consists of the advection phase and non-advection phase. The former employs the Rational function CIP scheme in order to preserve monotone signals, and the latter is solved by interpolated differential operator scheme for achieving the accurate calculation. The procedure is categorized into the fractionally stepped semi-Lagrangian. The accuracy of our scheme is confirmed by checking the one-dimensional plane shock tube problem with 103 times initial density and pressure jump in comparison with the analytic solution. The Sedov,Taylor blast wave problem is also examined in the two-dimensional cylindrical coordinate in order to check the spherical symmetry and the convergence rates. Two- and three-dimensional simulations for the blast waves from the explosion in the underground magazine are carried out. It is found that the numerical results show quantitatively good agreement with the experimental data. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Exact steady periodic water waves with vorticity

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 4 2004
Adrian Constantin
We consider the classical water wave problem described by the Euler equations with a free surface under the influence of gravity over a flat bottom. We construct two-dimensional inviscid periodic traveling waves with vorticity. They are symmetric waves whose profiles are monotone between each crest and trough. We use bifurcation and degree theory to construct a global connected set of such solutions. © 2003 Wiley Periodicals, Inc. [source]

Required source distribution for interferometry of waves and diffusive fields

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2009
Yuanzhong Fan
SUMMARY The Green's function that describes wave propagation between two receivers can be reconstructed by cross-correlation provided that the receivers are surrounded by sources on a closed surface. This technique is referred to as ,interferometry' in exploration seismology. The same technique for Green's function extraction can be applied to the solution of the diffusion equation if there are sources throughout in the volume. In practice, we have only a finite number of active sources. The issues of the required source distribution is investigated, as is the feasibility of reconstructing the Green's function of the diffusion equation using a limited number of sources within a finite volume. We study these questions for homogeneous and heterogeneous media for wave propagation and homogeneous media for diffusion using numerical simulations. These simulations show that for the used model, the angular distribution of sources is critical in wave problems in homogeneous media. In heterogeneous media, the position and size of the heterogeneous area with respect to the sources determine the required source distribution. For diffusion, the sensitivity to the sources decays from the midpoint between the two receivers. The required width of the source distribution decreases with frequency, with the result that the required source distribution for early- and late-time reconstruction is different. The derived source distribution criterion for diffusion suggests that the cross-correlation-based interferometry is difficult to apply in field condition. [source]

Solution of non-linear dispersive wave problems using a moving finite element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2007
Abigail Wacher
Abstract The solution of the fully non-linear time-dependent two-dimensional shallow water equations is considered. Dispersive effects due to the Coriolis forces are taken into account. Such effects are of major importance in geophysical fluid dynamics applications. The recently proposed string gradient weighted moving finite element method is extended for this class of problems. This method simultaneously determines, at each time step, the solution of the governing partial differential equations and an optimal location of the finite element nodes. It has previously been applied to non-dispersive wave problems; here its performance under the demanding conditions of large Coriolis forces, inducing large mesh and field rotation, is studied. Optimal rates of convergence are obtained. Results for some example problems of water hump release are presented. Non-linear and linearized solutions are compared. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Coupling of mapped wave infinite elements and plane wave basis finite elements for the Helmholtz equation in exterior domains

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2003
Rie Sugimoto
Abstract The theory for coupling of mapped wave infinite elements and special wave finite elements for the solution of the Helmholtz equation in unbounded domains is presented. Mapped wave infinite elements can be applied to boundaries of arbitrary shape for exterior wave problems without truncation of the domain. Special wave finite elements allow an element to contain many wavelengths rather than having many finite elements per wavelength like conventional finite elements. Both types of elements include trigonometric functions to describe wave behaviour in their shape functions. However the wave directions between nodes on the finite element/infinite element interface can be incompatible. This is because the directions are normally globally constant within a special finite element but are usually radial from the ,pole' within a mapped wave infinite element. Therefore forcing the waves associated with nodes on the interface to be strictly radial is necessary to eliminate this internode incompatibility. The coupling of these elements was tested for a Hankel source problem and plane wave scattering by a cylinder and good accuracy was achieved. This paper deals with unconjugated infinite elements and is restricted to two-dimensional problems. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009
A. El Kacimi
Abstract In this paper, we investigate a numerical approach based on the partition of unity finite element method, for the time-harmonic elastic wave equations. The aim of the proposed work is to accurately model two-dimensional elastic wave problems with fewer elements, capable of containing many wavelengths per nodal spacing, and without refining the mesh at each frequency. The approximation of the displacement field is performed via the standard finite element shape functions, enriched by superimposing pressure and shear plane wave basis, which incorporate knowledge of the wave propagation. A variational framework able to handle mixed boundary conditions is described. Numerical examples dealing with the radiation and the scattering of elastic waves by a circular body are presented. The results show the performance of the proposed method in both accuracy and efficiency. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A numerical integration scheme for special finite elements for the Helmholtz equation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003
Peter Bettess
Abstract The theory for integrating the element matrices for rectangular, triangular and quadrilateral finite elements for the solution of the Helmholtz equation for very short waves is presented. A numerical integration scheme is developed. Samples of Maple and Fortran code for the evaluation of integration abscissæ and weights are made available. The results are compared with those obtained using large numbers of Gauss,Legendre integration points for a range of testing wave problems. The results demonstrate that the method gives correct results, which gives confidence in the procedures, and show that large savings in computation time can be achieved. Copyright © 2002 John Wiley & Sons, Ltd. [source]

The performance of spheroidal infinite elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2001
R. J. Astley
Abstract A number of spheroidal and ellipsoidal infinite elements have been proposed for the solution of unbounded wave problems in the frequency domain, i.e solutions of the Helmholtz equation. These elements are widely believed to be more effective than conventional spherical infinite elements in cases where the radiating or scattering object is slender or flat and can therefore be closely enclosed by a spheroidal or an ellipsoidal surface. The validity of this statement is investigated in the current article. The radial order which is required for an accurate solution is shown to depend strongly not only upon the type of element that is used, but also on the aspect ratio of the bounding spheroid and the non-dimensional wave number. The nature of this dependence can partially be explained by comparing the non-oscillatory component of simple source solutions to the terms available in the trial solution of spheroidal elements. Numerical studies are also presented to demonstrate the rates at which convergence can be achieved, in practice, by unconjugated-(,Burnett') and conjugated (,Astley-Leis')-type elements. It will be shown that neither formulation is entirely satisfactory at high frequencies and high aspect ratios. Copyright © 2001 John Wiley & Sons, Ltd. [source]