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Computational Methods for Fluid Dynamics, 2019
The SWE are a system of two nonlinear hyperbolic PDEs that must be numerically solved to describe the time evolution of the fluid velocity and water depth in the entire computational domain. Finite-difference methods to obtain approximate numerical solutions are described in this chapter. First, basic numerical aspects are presented. The implementation
J. Ferziger, M. Peric, R. Street
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The SWE are a system of two nonlinear hyperbolic PDEs that must be numerically solved to describe the time evolution of the fluid velocity and water depth in the entire computational domain. Finite-difference methods to obtain approximate numerical solutions are described in this chapter. First, basic numerical aspects are presented. The implementation
J. Ferziger, M. Peric, R. Street
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P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method
, 1986I present a finite-difference method for modeling P-SV wave propagation in heterogeneous media. This is an extension of the method I previously proposed for modeling SH-wave propagation by using velocity and stress in a discrete grid.
J. Virieux
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Finite Difference Schemes and Partial Differential Equations
, 1989Preface to the second edition Preface to the first edition 1. Hyperbolic partial differential equations 2. Analysis of finite difference Schemes 3. Order of accuracy of finite difference schemes 4. Stability for multistep schemes 5.
J. Strikwerda
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Dispersion-relation-preserving finite difference schemes for computational acoustics
, 1993Acoustics problems are governed by the linearized Euler equations. According to wave propagation theory, the number of wave modes and their wave propagation characteristics are all encoded in the dispersion relations of the governing equations.
C. Tam, J. Webb
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Finite-difference methods [PDF]
, 2001 In previous chapters, we have discussed the equations governing the structure of a steady flow and the evolution of an unsteady flow, and derived selected solutions for elementary flow configurations by analytical and simple numerical methods. To generate solutions for arbitrary flow conditions and boundary geometries, it is necessary to develop ...
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Acta Mathematica Hungarica, 1998
Let \(A\) denote a finite subset of \({\mathbb{R}}^n\). The difference set of \(A\) is given by \(A-A=\{a-b:a,b\in A\}\). The affine dimension of \(A\), denoted by \(d=\dim A\), is defined as the dimension of the smallest affine subspace containing \(A\). \textit{G. A. Freiman}, \textit{A. Heppes}, and \textit{B. Uhrin} derived the general lower bound \
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Let \(A\) denote a finite subset of \({\mathbb{R}}^n\). The difference set of \(A\) is given by \(A-A=\{a-b:a,b\in A\}\). The affine dimension of \(A\), denoted by \(d=\dim A\), is defined as the dimension of the smallest affine subspace containing \(A\). \textit{G. A. Freiman}, \textit{A. Heppes}, and \textit{B. Uhrin} derived the general lower bound \
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Journal of Computational Physics, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Finite Differences and Finite Elements
2011In the preceding chapters, we have described the numerical solution techniques most commonly applied in ocean-acoustic propagation modeling. One or more of these approaches are numerically efficient for the majority of forward problems occurring in underwater acoustics, including propagation over very long ranges, with or without lateral variations in ...
Michael B. Porter +3 more
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2001
The finite difference method is a universally applicable numerical method for the solution of differential equations. In this chapter, for a sample parabolic partial differential equation, we introduce some difference schemes and analyze their convergence. We present the well-known Lax equivalence theorem and related theoretical results, and apply them
Kendall Atkinson, Weimin Han
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The finite difference method is a universally applicable numerical method for the solution of differential equations. In this chapter, for a sample parabolic partial differential equation, we introduce some difference schemes and analyze their convergence. We present the well-known Lax equivalence theorem and related theoretical results, and apply them
Kendall Atkinson, Weimin Han
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, 2007
Finite difference approximations -- Steady states and boundary value problems -- Elliptic equations -- Iterative methods for sparse linear systems -- The initial value problem for ordinary differential equations -- Zero-stability and convergence for ...
R. LeVeque
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Finite difference approximations -- Steady states and boundary value problems -- Elliptic equations -- Iterative methods for sparse linear systems -- The initial value problem for ordinary differential equations -- Zero-stability and convergence for ...
R. LeVeque
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