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2013 | OriginalPaper | Buchkapitel

3. Introduction to Computational Fluid Dynamics and Ocean Modelling

verfasst von : Tomas Torsvik

Erschienen in: Preventive Methods for Coastal Protection

Verlag: Springer International Publishing

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Abstract

This chapter provides a short introduction to the most commonly used numerical methods in computational fluid dynamics, and some specific aspects of numerical modelling of ocean currents. When working with numerical models, it is essential to have a basic understanding of the possibilities and limitations of the modelling toolbox. The first part gives a demonstration on how the model differential equations for fluid motions can be transformed into computer code instructions. Important concepts such as consistency, stability and convergence are discussed. The second part of the chapter provides an introduction to ocean modelling, with emphasis on the approximations that are commonly used in general circulation models.

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Fußnoten
1
In Eq. (3.5) the expression f (j)(x 0) indicates the j-th derivative of the function f, not to be confused with the discretization notation f (n).
 
2
The ‘Big O’ notation describes the limiting behaviour of a function f by comparing it to the behaviour of a simpler function g. Therefore, if
$$\lim_{x \rightarrow x_0} \frac{f(x)}{g(x)} = C $$
where C is some finite number, then \(f(x) = \mathcal{O}(g(x))\) as xx 0. When discussing finite difference schemes it is implicitly understood that the approximation is valid for Δx→0, and therefore this condition is usually not stated explicitly in the formulas.
 
3
Note that the rotation of the Earth is not a driving force in itself. When Newton’s laws of motion are applied in a rotating frame of reference, motion along a straight line appears to be deflected to the left or right. The Coriolis and centrifugal forces are introduced to account for such deflections. These forces are often called inertial forces or fictitious forces in order to emphasize that they are not connected to any physical force, but to the acceleration of the rotating system itself.
 
5
M.I.T. general circulation model, http://​mitgcm.​org/​.
 
7
Regional Ocean Modeling System, http://​www.​myroms.​org/​.
 
8
Miami Isopycnic Coordinate Ocean Model.
 
10
HYbrid Coordinate Ocean Model, http://​hycom.​org/​.
 
11
Finite Volume Coastal Ocean Model, http://​fvcom.​smast.​umassd.​edu/​FVCOM/​.
 
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Metadaten
Titel
Introduction to Computational Fluid Dynamics and Ocean Modelling
verfasst von
Tomas Torsvik
Copyright-Jahr
2013
Verlag
Springer International Publishing
DOI
https://doi.org/10.1007/978-3-319-00440-2_3