| Description |
1 online resource (626 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
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Print version record. |
| Contents |
Front Cover; Semi-Lagrangian Advection Methods and Their Applications in Geoscience; Copyright; Contents; 1 Introduction; 2 Eulerian modeling of advection problems; 2.1 Continuous form of the advection equation; 2.1.1 Derivation of the one-dimensional Eulerian advection equation; Mass conservation derivation of the advection equation; Taylor series expansion derivation of the one-dimensional advection equation; 2.1.2 Methods of characteristics; 2.2 Finite difference approximations to the Eulerian formulation of the advection equation; 2.2.1 Upwind forward Euler |
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Upwind forward Euler with the bell curveUpwind forward Euler with the step function; 2.2.2 Forward-time, centered-space, FTCS; 2.2.3 Lax-Friedrichs scheme; 2.2.4 Lax-Wendroff scheme; 2.2.5 Leap-frog, centered-time-centered-space (CTCS); 2.2.6 Linear multistep methods: Adams-Bashforth schemes; 2.2.7 Explicit Runge-Kutta methods; Derivation of the general explicit fourth-order Runge-Kutta method; 2.3 Implicit schemes; 2.3.1 Implicit, or backward Euler, scheme; 2.3.2 Crank-Nicolson scheme; 2.3.3 Box scheme; 2.3.4 Adams-Moulton methods; 2.3.5 Backward differentiation formula |
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2.3.6 Implicit Runge-Kutta methodsImplicit midpoint derivation; Implicit trapezoidal derivation; Collocated implicit Runge-Kutta schemes; 2.3.7 Diagonally implicit Runge-Kutta schemes (DIRK); 2.4 Predictor-corrector methods; 2.4.1 Adams-Bashforth-Adams-Moulton predictor-corrector; 2.5 Summary; 3 Stability, consistency, and convergence of Eulerian advection based numerical methods; 3.1 Truncation error; 3.1.1 Consistency; 3.1.2 Truncation errors and consistency analysis of the linear multistep methods; 3.2 Dispersion and dissipation errors; 3.3 Amplitude and phase errors; 3.4 Stability |
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3.4.1 Courant-Friedrichs-Lewy condition3.4.2 Von Neumann stability analysis; 3.4.3 Multistep method stability; 3.5 Quantifying the properties of the explicit nite difference schemes; 3.5.1 Upwind forward Euler scheme; 3.5.2 Forward-time-centered-space scheme; 3.5.3 Lax-Friedrichs scheme; 3.5.4 Lax-Wendroff scheme; 3.5.5 Leap-frog, centered-time-centered-space scheme; 3.6 Linear multistep methods; 3.6.1 Stability of Adams-Bashforth 2 scheme; 3.7 Consistency and stability of explicit Runge-Kutta methods; 3.8 Implicit schemes; 3.8.1 Backward Euler scheme; 3.8.2 Crank-Nicolson scheme |
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3.9 Predictor-corrector methods3.10 Summary; 4 History of semi-Lagrangian methods; 4.1 Fjørtoft (1952) paper; 4.1.1 Barotropic problem; 4.1.2 The problem with time integration; 4.2 Welander (1955) paper; 4.3 Wiin-Nielsen (1959) paper; 4.4 Robert's (1981) paper; 4.5 Summary; 5 Semi-Lagrangian methods for linear advection problems; 5.1 Derivation of the Lagrangian form for advection; 5.2 Derivation of the semi-Lagrangian approach; 5.3 Semi-Lagrangian advection of the bell curve; 5.3.1 Semi-Lagrangian advection using linear Lagrange interpolation |
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5.3.2 Quadratic Lagrange interpolation polynomial |
| Subject |
Earth sciences -- Mathematical models.
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Lagrange equations.
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Sciences de la terre -- Modèles mathématiques.
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Équations de Lagrange.
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Earth sciences -- Mathematical models
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Lagrange equations
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| Other Form: |
Print version: Fletcher, Steven J. Semi-Lagrangian Advection Methods and Their Applications in Geoscience. San Diego : Elsevier, ©2019 9780128172223 |
| ISBN |
0128172231 |
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9780128172230 (electronic bk.) |
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9780128172223 |
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0128172223 |
| Standard No. |
AU@ 000066283570 |
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