Numerical Modeling Of Wave Propagation Research Articles

Instability and dispersivity of wave propagation in inelastic saturated/unsaturated porous media

A model based on the Biot theory for simulating coupled hydro-dynamic behavior in saturated-unsaturated porous media was utilized with integration of the inertial coupling effect between the solid-fluid phases of the media into the model. Stationary instability and dispersivity of wave propagation in the media in one-dimensional problem were analyzed. The effects of the following factors on stationary instability and dispersivity were discussed. They are the viscous and inertial couplings between the solid and the fluid phases, compressibility of the mixture composed of solid grains and pore fluid, the degree of saturation, visco-plastic (rate dependent inelastic) constitutive behavior of the solid skeleton under high strain rate. The results and conclusion obtained by the present work will provide some bases or clues for overcoming the difficulties in numerical modelling of wave propagation in the media subjected to strong and shock loading.

Perfectly matched layer truncation for parabolic wave equation models

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Levy Mireille F. 2001Perfectly matched layer truncation for parabolic wave equation modelsProc. R. Soc. Lond. A.4572609–2624http://doi.org/10.1098/rspa.2001.0848SectionRestricted accessResearch articlePerfectly matched layer truncation for parabolic wave equation models Mireille F. Levy Mireille F. Levy Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK Google Scholar Find this author on PubMed Search for more papers by this author Mireille F. Levy Mireille F. Levy Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 November 2001https://doi.org/10.1098/rspa.2001.0848AbstractSolutions of the parabolic wave equation are extended to complex values of the height variable. The fast decay of the solutions in certain directions of the complex plane is used to improve parabolic wave equation solvers: the solution is marched on a suitably chosen contour in the complex plane rather than on the real line. This interpretation of Bérenger's perfectly matched layer allows extremely efficient truncation of the computational domain with a split–step/Fourier algorithm. The theory is developed for both the wide–angle and narrow–angle parabolic wave equations, and numerical results are presented. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Petrov P, Ehrhardt M, Tyshchenko A and Petrov P (2020) Wide-angle mode parabolic equations for the modelling of horizontal refraction in underwater acoustics and their numerical solution on unbounded domains, Journal of Sound and Vibration, 10.1016/j.jsv.2020.115526, 484, (115526), Online publication date: 1-Oct-2020. Ramamurti A and Calvo D (2019) Multisector parabolic-equation approach to compute acoustic scattering by noncanonically shaped impenetrable objects, Physical Review E, 10.1103/PhysRevE.100.063309, 100:6 Scrinzi A, Stimming H and Mauser N (2014) On the non-equivalence of perfectly matched layers and exterior complex scaling, Journal of Computational Physics, 10.1016/j.jcp.2014.03.007, 269, (98-107), Online publication date: 1-Jul-2014. Chen H, Zhou H, Lin H and Wang S (2013) Application of perfectly matched layer for scalar arbitrarily wide-angle wave equations, GEOPHYSICS, 10.1190/geo2012-0062.1, 78:1, (T29-T39), Online publication date: 1-Jan-2013. Sheng Q and Sun H (2015) Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers, Communications in Computational Physics, 10.4208/cicp.100811.090112a, 12:4, (1275-1292), Online publication date: 1-Oct-2012. Chen H, Zhou H, Lin H and Wang S (2012) Application of perfectly matched layer for scalar arbitrarily wide-angle wave equations SEG Technical Program Expanded Abstracts 2012, 10.1190/segam2012-0452.1, , (1-5), Online publication date: 1-Sep-2012. Ozbayat S and Janaswamy R Effective Local Absorbing Boundary Conditions for a Finite Difference Implementation of the Parabolic Equation, IEEE Transactions on Antennas and Propagation, 10.1109/TAP.2011.2122300, 59:5, (1616-1625) Heidari A and Guddati M (2006) Highly accurate absorbing boundary conditions for wide-angle wave equations, GEOPHYSICS, 10.1190/1.2192914, 71:3, (S85-S97), Online publication date: 1-May-2006. von Winckel G, Krishna S and Coutsias E (2006) Spectral element modeling of semiconductor heterostructures, Mathematical and Computer Modelling, 10.1016/j.mcm.2005.05.028, 43:5-6, (582-591), Online publication date: 1-Mar-2006. Hagstrom T (2003) New Results on Absorbing Layers and Radiation Boundary Conditions Topics in Computational Wave Propagation, 10.1007/978-3-642-55483-4_1, (1-42), . Pled F and Desceliers C (2021) Review and Recent Developments on the Perfectly Matched Layer (PML) Method for the Numerical Modeling and Simulation of Elastic Wave Propagation in Unbounded Domains, Archives of Computational Methods in Engineering, 10.1007/s11831-021-09581-y This Issue08 November 2001Volume 457Issue 2015 Article InformationDOI:https://doi.org/10.1098/rspa.2001.0848Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/11/2001Published in print08/11/2001 License: Citations and impact Keywordswave equationparabolic equation modelselectromagnetic scatteringperfectly matched layer

Stationary discontinuity and flutter instability of wave propagation in elasto-plastic saturated porous media

In the present work a model based on the Biot theory for simulating coupled hydrodynamic behavior in saturated porous media is utilized with integration of the inertial coupling effect between the solid-fluid phases of the media into the model. The non-associated Drucker-Prager criterion to describe nonlinear constitutive behavior of pressure dependent elasto-plasticity for the media is particularly considered. With no consideration of compressibility of solid grains and the pore fluid, the discontinuity and instability of the wave propagation in saturated porous media are analyzed for the plane strain problems in detail. The critical conditions of stationary discontinuity and flutter instability in the wave propagation are given. The results and conclusions obtained by the present work will provide some bases or clues for overcoming the difficulties in numerical modeling of wave propagation in the media subjected to dynamic loading.

The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media

The perfectly matched layer (PML) was first introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. In this paper, a method is developed to extend the perfectly matched layer to simulating seismic wave propagation in poroelastic media. This nonphysical material is used at the computational edge of a finite‐difference algorithm as an ABC to truncate unbounded media. The incorporation of PML in Biot’s equations is different from other PML applications in that an additional term involving convolution between displacement and a loss coefficient in the PML region is required. Numerical results show that the PML ABC attenuates the outgoing waves effectively.

Improvement on open boundaries on a time dependent numerical model of wave propagation in the nearshore region

An improvement on the simulation of outgoing waves on a time dependent numerical model for water wave propagation in the nearshore region is presented. The governing equations consist of a system of first order partial differential equations (PDEs), the equation of continuity and the equation of motion. A comparative study of first order radiation boundary conditions (BCs) and first order radiation BCs combined with sponge layers is presented for cases where outgoing waves leave the numerical domain of calculation through the open boundary. A reduction of spurious reflections from the numerical open boundaries can be obtained with an irrelevant increase in terms of computational cost.

A whole surf zone modelling approach as an aid to investigation of nearshore and coastal morphodynamics

Studies of the theoretical relationships between wave characteristics, nearshore topography and beach dynamics are common in coastal engineering and coastal geomorphology studies. Frequently, these studies use spatially averaged values of dynamic variables (waves, tides) and spatially-averaged nearshore topography. Such an approach reduces the accuracy and introduces errors when the relationships between variables are considered. High-resolution surf-zone Input and output which are needed to simulate the complex relationships between waves, tides, winds and sediments for both modal and high energy/low frequency events can, however, be achieved by adapting and extending existing approaches. This paper introduces a method to investigate and characterise wave-induced processes using a whole-surf-zone approach (i.e. an integrated rather than an averaged approach) and produce useful output for geomorphological interpretation of beach morphodynamics. This involves the following steps: (i) Extraction of spatially-referenced hydrodynamic data from a 2-D numerical wave propagation model. The geographical and hydrodynamic data is then written to a secondary file. (ii) Creation of a surf-zone map and hydrodynamic database. (iii) Calculation of(a) local slopes within the surf-zone to characterise nearshore processes and (b) average slopes for application of beach classification formulae (eg. surf scaling parameter). (iv) Calculation of nearshore parameters (eg. potential currents, sediment transport, wave setup etc). (v) Extraction of G.I.S. compatible output for further analyses. This approach, while still a simplification of surf-zone processes, avoids the surf-zone averaging or single-point data limitations inherent in earlier approaches and offers the opportunity for more robust and detailed investigations of nearshore processes. It also avoids the bathymetric updating of other models, which tend to multiply errors. Several examples are discussed in which the use of this approach as an aid to morphodynamic interpretation has been demonstrated. The approach is presented as an aid to interpretation of field observations through simulation of relevant morphodynamic parameters which would be difficult to obtain through field measurement.

Validation des calculs de propagation d'ondes: approches par éléments finis et éléments de frontière

ABSTRACT This paper presents several aspects of the validation of wave propagation computations. The numerical modelling of wave propagation is discussed through two different approaches: the finite element method and the boundary element method. Wave propagation involves specific phenomena such as damping and dispersion. For computations of wave propagation by the finite element method, similar properties, artificial and purely numerical, arise: numerical dispersion and numerical damping. The influence of the mesh refinement on wave propagation computations (1D and 2D) is discussed and quantified for different finite element types (triangular, quadrilateral, higher order). The numerical modelling of damping is also investigated (Rayleigh damping). For the boundary element method, two validation examples are presented: the first one is related to an exact analytical solution, the second one to seismic in situ experiments.

S band Doppler radar measurements of bathymetry, wave energy fluxes, and dissipation across an offshore bar

The use of a shore‐based microwave Doppler radar for the remote sensing of ocean wave propagation over an offshore sand bar was investigated. The radar yielded high spatial resolution measurements of several quantities of importance in the study of bar dynamics. The spatial variation in wave phase with distance along the radar beam direction was used to calculate bathymetry with sufficient accuracy and resolution to clearly reveal the presence of the bar and the tidal cycle variation of water depth. This real‐time bathymetry enabled the calculation of ocean wave energy fluxes from the radar velocity data. These energy fluxes showed good agreement with predictions from a numerical wave propagation model, except in regions of significant wave breaking, where the discrepancy between measured and modeled fluxes was found to be closely related to the modeled wave dissipation rate.

Attenuating boundary conditions for numerical modeling of acoustic wave propagation

Four types of boundary conditions: Dirichlet, Neumann, transmitting, and modified transmitting, are derived by combining the damped wave equation with corresponding boundary conditions. The Dirichlet attenuating boundary condition is the easiest to implement. For an appropriate choice of attenuation parameter, it can achieve a boundary reflection coefficient of a few percent in a one‐wavelength wide zone. The Neumann‐attenuating boundary condition has characteristics similar to the Dirichlet attenuating boundary condition, but it is numerically more difficult to implement. Both the transmitting boundary condition and the modified transmitting boundary condition need an absorbing boundary condition at the termination of the attenuating region. The modified transmitting boundary condition is the most effective in the suppression of boundary reflections. For multidimensional modeling, there is no perfect absorbing boundary condition, and an approximate absorbing boundary condition is used.

Numerical Modelling of Wave Propagation in Elastic Rectangular Block Media

Novel formulations for numerical modelling of elastic waves in block media are developed in this paper. A single differential-difference equation, which can be discretized to give explicit finite difference models of wave propagation in elastic block media, is obtained after incorporating continuity conditions of stresses into the equation of motion. Further decompositions of the differential-difference equation also lead to a parallel algorithm for computing the wave field.

Numerical modeling of elastic wave propagation in anisotropic materials : You, Z.; Lord, W.; Ludwig, R. Review of Progress in Quantitative Nondestructive Evaluation, Williamsburg, Virginia (United States), 22–26 Jun. 1987. Vol. 7A, pp. 23–30. Edited by D.D. Thompson and D.E. Chimenti, Plenum Press, 1988

Numerical modeling of elastic wave propagation in anisotropic materials : You, Z.; Lord, W.; Ludwig, R. Review of Progress in Quantitative Nondestructive Evaluation, Williamsburg, Virginia (United States), 22–26 Jun. 1987. Vol. 7A, pp. 23–30. Edited by D.D. Thompson and D.E. Chimenti, Plenum Press, 1988

Passage of a powerful HF radio wave through the lower ionosphere as a function of initial electron density profiles

The results of numerical modelling of powerful HF radio wave propagation through the ionosphere plasma are presented. Comparison of the heating wave parameters with those of a low powerwave gives the possibility to study the self-action of the powerful HF wave. At low altitudes the ‘translucence’ of the ionosphere plasma takes place. At high altitudes the wave absorption sharply increases. Both self-action effects lead to the reduction of the altitude range of the heated region. The dependence of self-action effects and the resulting electron temperature profiles on the initial electron density profiles are studied.

Numerical modeling of elastic wave propagation and scattering with EFIT — elastodynamic finite integration technique

The basic equations of EFIT, the Elastodynamic Finite Integration Technique, are formulated for anisotropic inhomogeneous media in 3D. For isotropie inhomogeneous media we discuss the discrete equations on a staggered grid resulting in a unique way to discretize material parameters, and evaluate stability conditions and consistency for isotropic homogeneous unbounded media. For the sake of simplified visualization, numerical results are presented for various two-dimensional problems as they originate from nondestructive testing applications. In particular, EFIT wavefronts are related to group velocity curves for anisotropic media with transverse isotropy and cubic symmetry, the latter one being derived by a coordinate-free approach in the appendix.

An optimal absorbing boundary condition for elastic wave modeling

Absorbing boundary conditions are widely used in numerical modeling of wave propagation in unbounded media to reduce reflections from artificial boundaries (Lindman, 1975; Clayton and Engquist, 1977; Reynolds, 1978; Liao et al., 1984; Cerjan et al., 1985; Randall, 1988; Higdon, 1991). We are interested in a particular absorbing boundary condition that has maximum absorbing ability with a minimum amount of computation and storage. This is practical for 3-D simulation of elastic wave propagation by a finite‐difference method. Peng and Toksöz (1994) developed a method to design a class of optimal absorbing boundary conditions for a given operator length. In this short note, we give a brief introduction to this technique, and we compare the optimal absorbing boundary conditions against those by Reynolds (1978) and Higdon (1991) using examples of 3-D elastic finite‐difference modeling on an nCUBE-2 parallel computer. In the Appendix, we also give explicit formulas for computing coefficients of the optimal absorbing boundary conditions.

MOORED SHIP PROBLEMS IN THE PORT OF CADIZ. ANALYSIS OF WAVE AND LONG WAVE ACTION

Several ro-ro and ferry vessels have suffered problems while moored in the Port of Cadiz during the last months. Large amplitude motions and breakage of mooring lines produce a serious decrease in the efficiency of load transfer or can even impede it, while safety is seriously threatened. A project study was developed which aimed to define the problem, describe the reasons which cause it and propose solutions. Wave measurements, observation of ship motions, numerical wave propagation models, as well as wave and moored ship physical models were applied to accomplish these objectives. This paper concentrates on the application of the physical model to define the wave and long wave conditions close to and inside the port, as well as the moored ship response in different situations.

Field experiments for characterization of GPR antenna and pulse propagation

Productive interpretations of ground penetrating radar surveys require an accurate understanding of electromagnetic wave radiation, propagation, and scattering in geological materials as well as accurate knowledge of the reflection characteristics of various target anomalies embedded in such materials. GPR responses and survey profiles are often interpreted on the basis of theoretical estimates and numerical simulation models of electromagnetic wave propagation in simplified representations of ground materials and by using idealized target contrasts and geometries. Alternatively, field experiments performed under controlled test conditions can also be effective in demostrating GPR system performance capabilities and in providing quantitative measurements in realistic geologic formations. Experimental research at the University of Rome “La Sapienza” and at the Italian National Research Council were initiated to develop a basic understanding of the radiation and scattering characteristics of VHF pulse-mode GPR signals in earth materials and in air with emphasis on antenna ground coupling and target backscatter responses. The results of the experimental measurements conducted in air provided baseline information on the GPR system and target reflections under lossless propagation conditions. Target response measurements at various burial depths provided a systematic data base from which target responses, propagation parameters of the medium, and relevant data processing techniques were evaluated to gain useful insights into their interpretations. Other more advanced experimental tests are planned for the future.

On the Origin of Parasitic Modes in Numerical Modelling of Wave Propagation in Plasmas

The mode mixing encountered in solving the boundary value problem arising in studies of wave propagation in hot one-dimensional plasmas is investigated. The wave differential equations, second order in ion Larmor radius, are shown to contain close to the ion cyclotron resonance an unwanted coupling mechanism, closely related to mode conversion driven by the equilibrium gradients. Consequently, the solution mixes with parasitic modes which carry power out of the resonance zone. In the case of strong coupling, this may lead to a generation of excess energy flux for complex valued coefficients of the wave equations. The importance and effects of this phenomenon are demonstrated in the special case of simulations of minority ion cyclotron heating in tokamaks. It is shown that the mode mixing can be avoided by adjusting the elements of the coefficient matrix of the wave equations, which makes the second-order system amenable to the problems with high minority concentration which is important for studies of fusion physics.

Numerical modelling of ultrasonic wave propagation using the efficient p-version finite element method

In this paper, the new p-version of the finite element method has been used for the numerical modelling of ultrasonic wave propagation in solid media. The p-method involves increasing the polynomial order of the interpolation functions to achieve convergence. This is unlike the conventional h-version in which the number of elements is increased to achieve the same goal. Illustrative examples of wave propagation through an isotropic aluminium block, including a case with a built-in defect in the form of a crack, have been discussed. Also, a convergence criterion has been developed for dynamic problems. The potential to extend this model to other applications such as medical ultrasonics or to a more complex anisotropic medium is significant.

Deformation of Nonlinear Waves on a Rectangular Step

ABSTRACTA numerical model for nonlinear wave propagation over a rectangular step is formulated by utilizing the boundary element method. The computation by this model gives a more realistic wave profile than that of linear wave theory. The model is used for study of the formation of higher harmonic components in the process of wave propagation over the step. In comparison with the results of laboratory experiments, the model gives good estimation of the amplitudes of the second and third harmonic components, and gives a over-prediction of the first harmonic component. Reflection and transmission coefficients are calculated by including these harmonic components in the computation of wave height. The model yields the coefficients in good agreement with the experimental results.In addition to the analysis of harmonic components, the energy loss in the process of wave propagation over the step was experimentally investigated. A Fiber Laser Velocimeter is used to measure the water particle velocity at about f...

Numerical modeling of wave propagation in optical nonlinear couplers

AbstractA numerical method is proposed and implemented for the analysis of propagation characteristics of nonlinear optical couplers. This technique is based on the shooting method. A fourth‐order Runge‐Kutta method is adopted to solve wave equations in the coupler. An error function is defined to estimate the discrepency between the computed and predicted boundary values. A secant method is then used to evaluate the correction term of the initial guesses. This procedure is performed iterationally for realization of nonlinear couplers with an arbitrary number of branches and varying parameters. © 1993 John Wiley & Sons, Inc.