Download or read book Stability Analysis of Finite Difference Schemes for the Viscoelastic Wave Equation written by and published by . This book was released on 1994 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is difficult to predict stability properties of a finite difference scheme. It has to be investigated through the roots of the Z-transformed and Fourier transformed difference scheme (modal equation). To simultaneously investigate several schemes for the viscoelastic wave equation, it is possible to derive the modal equation with parameterized coefficients. Several conditionally stable schemes were found, where the most efficient is a staggered scheme with a stability condition closely resembling that of an elastic scheme.
Download or read book Wave Propagation and Stability for Finite Difference Schemes written by L. N. Trefethen and published by . This book was released on 1982 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation investigates the behavior of finite difference models of linear hyperbolic partial differential equations. Whereas a hyperbolic equation is nondispersive and nondissipative, difference models are invariably dispersive, and often dissipative too. We set about analyzing them by means of existing techniques from the theory of dispersive wave propagation, making extensive use in particular of the concept of group velocity, the velocity at which energy propagates. The first three chapters present a general analysis of wave propagation in difference models. We describe systematically the effects of dispersion on numerical errors, for both smooth and parasitic waves. The reflection and transmission of waves at boundaries and interfaces are then studied at length. The key point for this is a distinction introduced here between leftgoing and rightgoing signals, which is based not on the characteristics of the original equation, but on the group velocities of the numerical model. The last three chapters examine stability for finite difference models of initial boundary value problems.
Download or read book Stress Wave Analysis in a Generalized Linear Viscoelastic Material Using Finite Differences and Characteristics written by Stephen Gerard Sawyer and published by . This book was released on 1970 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: An explicit finite difference scheme for solving the one-dimensional wave equation for a generalized linear viscoelastic solid has been derived. An accurate solution near the wave front is obtained by placing the nodal points of the finite difference grid along the characteristics of the wave equation. The viscoelastic properties of the solid are represented in terms of a generalized Voigt model. A FORTRAN IV program based on this scheme has been used to calculate the response to a step pulse, a triangular pulse, and a pulse which varies like (1-cos(ct)). In all cases, the calculated results are free of spurious oscillations which occur in certain other methods of numerical calculation, notably the extended Ritz method. (Author).
Download or read book The Finite Difference Modelling of Earthquake Motions written by Peter Moczo and published by Cambridge University Press. This book was released on 2014-04-24 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate students in earthquake seismology, computational and numerical modelling, and applied mathematics.
Download or read book An Interactive Visual Study of Finite Difference Stability of the 1 D Wave Equation in Time and Frequency Domains written by Jenny F. Ji and published by . This book was released on 1992 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Trends in Wave Mechanics and Vibrations written by S. Chakraverty and published by Springer Nature. This book was released on 2019-11-12 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of select proceedings of the National Conference on Wave Mechanics and Vibrations (WMVC 2018). It covers recent developments and cutting-edge methods in wave mechanics and vibrations applied to a wide range of engineering problems. The book presents analytical and computational studies in structural mechanics, seismology and earthquake engineering, mechanical engineering, aeronautics, robotics and nuclear engineering among others. This book can be useful for students, researchers, and professionals interested in the wide-ranging applications of wave mechanics and vibrations.
Download or read book Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations written by Gary Cohen and published by Springer. This book was released on 2016-08-05 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem of its spurious-free approximations. Treatment of unbounded domains by Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML) is described and analyzed in a separate chapter. The two last chapters deal with time approximation including local time-stepping and with the study of some complex models, i.e. acoustics in flow, gravity waves and vibrating thin plates. Throughout, emphasis is put on the accuracy and computational efficiency of the methods, with attention brought to their practical aspects.This monograph also covers in details the theoretical foundations and numerical analysis of these methods. As a result, this monograph will be of interest to practitioners, researchers, engineers and graduate students involved in the numerical simulationof waves.
Download or read book Stability of Finite Difference Approximations of Two Fluid Two Phase Flow Equations written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that the basic single pressure, two fluid model for two phase flow has complex characteristics and is dynamically unstable. Nevertheless, common nuclear reactor thermal-hydraulics codes use variants of this model for reactor safety calculations. In these codes, the non-physical instabilities of the model may be damped by the numerical method and/or additional momentum interchange terms. Both of these effects are investigated using the linearized Von Neumann stability analysis. The stability of the semi-implicit method is of primary concern, because of its computational efficiency and popularity. It is shown that there is likely no completely stable numerical method, including fully implicit methods, for the basic single pressure model. Additionally, the momentum interchange terms commonly added to the basic single pressure model do not result in stable numerical methods for all the physically interesting reference conditions. Although practical stable approximations may be realized on a coarse computational grid, it is concluded that the assumption of instantaneously equilibrated phasic pressures must be relaxed in order to develop a generally stable numerical solution of a two fluid model. The numerical stability of the semi-implicit discretization of the true two pressure models of Ransom and Hicks, and Holm and Kupershmidt is analyzed. The semi-implicit discretization of these models, which possess real characteristics, are found to be numerically stable as long as certain convective limits are satisfied. Based on the form of these models, the general form of a numerically stable, basic two pressure model is proposed. The evolution equation required for closure is a volume fraction transport equation, which may possibly be determined based on void wave propagation considerations. 43 refs., 22 figs., 3 tabs.
Download or read book Wave Fields in Real Media written by José M. Carcione and published by Elsevier. This book was released on 2014-12-08 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by the internationally renowned José M. Carcione, Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media examines the differences between an ideal and a real description of wave propagation, starting with the introduction of relevant stress-strain relations. The combination of this relation and the equations of momentum conservation lead to the equation of motion. The differential formulation is written in terms of memory variables, and Biot's theory is used to describe wave propagation in porous media. For each rheology, a plane-wave analysis is performed in order to understand the physics of wave propagation. This book contains a review of the main direct numerical methods for solving the equation of motion in the time and space domains. The emphasis is on geophysical applications for seismic exploration, but researchers in the fields of earthquake seismology, rock acoustics, and material science - including many branches of acoustics of fluids and solids - may also find this text useful. New to this edition: This new edition presents the fundamentals of wave propagation in Anisotropic, Anelastic, Porous Media while also incorporating the latest research from the past 7 years, including that of the author. The author presents all the equations and concepts necessary to understand the physics of wave propagation. These equations form the basis for modeling and inversion of seismic and electromagnetic data. Additionally, demonstrations are given, so the book can be used to teach post-graduate courses. Addition of new and revised content is approximately 30%. Examines the fundamentals of wave propagation in anisotropic, anelastic and porous media Presents all equations and concepts necessary to understand the physics of wave propagation, with examples Emphasizes geophysics, particularly, seismic exploration for hydrocarbon reservoirs, which is essential for exploration and production of oil
Download or read book Conservative Finite Difference Schemes For Regularized Long wave Equation written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1972 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Finite Difference Method for Analyzing the Compression of Poro viscoelastic Media written by George Joseph Habetler and published by . This book was released on 1970 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 1460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book A Comparison of Finite Difference Schemes Applied to the Wave Equation written by Kenneth E. Dickens and published by . This book was released on 1979 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Second International Conference on Mathematical and Numerical Aspects of Wave Propagation written by Ralph Kleinman and published by Soc for Industrial & Applied Math. This book was released on 1993 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Analysis of Accuracy of Finite Difference and Finite Element Methods for the Wave Equation written by Marvin Minei and published by . This book was released on 1988 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, Fourier analysis is used to investigate various approximation methods for the one- and two-dimensional wave equations. The spatial derivatives are approximated by the second order centered finite difference method, the linear and quadratic finite element methods, and the fourth order centered finite difference method. The approximation schemes thus obtained shall be continuous in time. Using Fourier analysis, their general solutions can be obtained. Group velocities of these solutions are then compared to the group velocity of the solution to the wave equation. These comparisons will yield a measure of accuracy for the approximation schemes. Finally, we obtain numerical computing schemes by using the second order centered finite difference method in time. Group velocities for these fully discrete schemes are also analyzed and the Courant number for each computing scheme will be shown to have an effect on its accuracy. In the one- and two-dimensional case, numerical results are given to back up the analysis.
Download or read book Fourth Order Symmetric Finite Difference Schemes for the Wave Equation written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
