swantech 手册.pdf

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SWAN SCIENTIFIC AND TECHNICAL DOCUMENTATION SWAN Cycle III version 40.91ABC

SWAN SCIENTIFIC AND TECHNICAL DOCUMENTATION by : The SWAN team mail address : Delft University of Technology Faculty of Civil Engineering and Geosciences Environmental Fluid Mechanics Section P.O. Box 5048 2600 GA Delft The Netherlands e-mail home page : : swan-info-citg@tudelft.nl http://www.swan.tudelft.nl Copyright (c) 1993-2013 Delft University of Technology. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back- Cover Texts. A copy of the license is available at http://www.gnu.org/licenses/fdl.html#TOC1.

Contents 1 Introduction 1.1 Historical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Purpose and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Readership . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Scope of this document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Acknowledgements 2 Governing equations 2.2.1 Wave kinematics 2.2.2 2.1 Spectral description of wind waves . . . . . . . . . . . . . . . . . . . . . . 2.2 Propagation of wave energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectral action balance equation . . . . . . . . . . . . . . . . . . . . 2.3 Sources and sinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 General concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Input by wind (Sin) . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Dissipation of wave energy (Sds) . . . . . . . . . . . . . . . . . . . . 2.3.4 Nonlinear wave-wave interactions (Snl) . . . . . . . . . . . . . . . . 2.3.5 First- and second-generation model formulations in SWAN . . . . . 2.4 Wave damping due to vegetation . . . . . . . . . . . . . . . . . . . . . . . 2.5 The inﬂuence of ambient current on waves . . . . . . . . . . . . . . . . . . 2.6 Modelling of obstacles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Reﬂection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.3 Diﬀraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Wave-induced set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Numerical approaches 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Discretization in geographical space . . . . . . . . . . . . . . . . . . 3.2.2 Note on the choice of geographic propagation schemes . . . . . . . . 3.2.3 Discretization in spectral space . . . . . . . . . . . . . . . . . . . . v 1 1 2 2 2 4 4 7 7 10 10 10 12 12 17 19 25 31 33 35 35 36 37 37 39 41 41 43 43 46 47

vi 3.3 Solution algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 An illustrative explanation of the sweeping approach . . . . . . . . . . . . Implementation of DIA within the four-sweep technique . . . . . . . . . . . 3.5 3.6 Convergence-enhancing measures . . . . . . . . . . . . . . . . . . . . . . . 3.7 Stopping criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Governing equations in curvilinear co-ordinates . . . . . . . . . . . . . . . 3.9 Computation of force in curvilinear co-ordinates . . . . . . . . . . . . . . . 3.10 Numerical treatment of obstacles . . . . . . . . . . . . . . . . . . . . . . . 3.11 Crossing of obstacle and grid line . . . . . . . . . . . . . . . . . . . . . . . 3.12 Integration over σ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.13 Transformation from relative to absolute frequency . . . . . . . . . . . . . 3.14 Interpolation of spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.15 Computation of breaking source term . . . . . . . . . . . . . . . . . . . . . 3.16 On the approximation of refraction on coarse grids in large-scale SWAN applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.16.2 The problem with refraction on coarse grids and how to deal with it 3.16.3 A historical overview of limitation on cθ . . . . . . . . . . . . . . . 4 Wave boundary and initial conditions 5 Implementation of 2D wave set-up 5.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Discretization of the 2D setup equation . . . . . . . . . . . . . . . . 5.2.2 The iterative solver for the linear system . . . . . . . . . . . . . . . 6 Iterative solvers 6.1 Strongly Implicit Procedure (SIP) . . . . . . . . . . . . . . . . . . . . . . . 6.2 Successive Over Relaxation (SOR) technique . . . . . . . . . . . . . . . . . 7 Parallel implementation aspects 7.1 Load balancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Parallelization of implicit propagation schemes . . . . . . . . . . . . . . . . 8 Unstructured mesh implementation 8.1 Description of an unstructured grid . . . . . . . . . . . . . . . . . . . . . . 8.1.1 Deﬁnitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 Relations between number of cells, vertices and faces . . . . . . . . 8.1.3 Conditions imposed to the grid . . . . . . . . . . . . . . . . . . . . 8.2 Some notes on grid generation . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Numerical method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Discretization procedure . . . . . . . . . . . . . . . . . . . . . . . . 48 51 54 54 56 58 60 61 63 63 64 65 66 68 68 68 72 75 77 77 78 78 84 87 87 88 89 89 90 93 93 93 94 94 95 95 95

8.3.2 The sweeping algorithm . . . . . . . . . . . . . . . . . . . . . . . . 99 Interpolation at user-deﬁned locations . . . . . . . . . . . . . . . . . . . . . 100 8.4 8.5 Computation of wave-induced force . . . . . . . . . . . . . . . . . . . . . . 102 8.6 Calculation of diﬀusion-like terms . . . . . . . . . . . . . . . . . . . . . . . 104 vii 9 The overall solution algorithm Bibliography Index 105 107 123

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