Titlebook: Numerical Methods for Shallow-Water Flow; C. B. Vreugdenhil Book 1994 Springer Science+Business Media B.V. 1994 Coast.Ocean.Storm.Storm su

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Behaviour of solutions,iscussed below in section 4.3). This implies that you can think of solutions as combinations of waves. The viscosity terms do have an influence: they will act as a damping mechanism. However, they are often not very large and you can generally assume that the wave properties are not essentially alte

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Boundary conditions,tions is closely related to the behaviour of characteristics if the system is hyperbolic. The SWE are hyperbolic if you do not take lateral friction into account. You can find the relevant theory in Courant & Hilbert (1962). It says first of all that the region of interest should be enclosed by a bo

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Time integration methods,all unknowns and . is a “mass matrix”; it is nontrivial in finite-element methods but is unity in most other cases. The number of equations equals the number of grid-point values and may be very large. Several standard numerical methods exist to integrate such systems of differential equations. They

explicit

Effects of time discretization on wave propagation,using the finite-difference analogue of (7.1):.(on the right-hand side, . is an exponent). The eigenvector v. of the matrix ... in (8.1) is the same as in the semi-discretized continuous-time case. The error is therefore characterized by comparing ρ. to exp(-.) with . and . is the wave frequency for

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Numerical treatment of boundary conditions, grid points around the central point. If applied at a boundary, you would need values from grid points located outside the region, which is impossible. Various approaches are possible to get additional equations on the boundary: