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| In our simulation <math>g = 1</math>, <math>L = 1</math>, <math>\varepsilon = 0.1</math>, <math>\rho = 1</math> and <math>H / \Delta x = 100</math>, where <math>\Delta x</math> is the initial distance between the particles. | | In our simulation <math>g = 1</math>, <math>L = 1</math>, <math>\varepsilon = 0.1</math>, <math>\rho = 1</math> and <math>H / \Delta x = 100</math>, where <math>\Delta x</math> is the initial distance between the particles. |
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| + | == Setting up the simulation == |
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| == References == | | == References == |
| <references /> | | <references /> |
Revision as of 14:14, 12 March 2015
Introduction
In this examples we are reproducing the simulation of the standing wave carried out by Souto et all (2012)
[1].
The standing wave is defined on top of an infinite periodic fluid domain composed by rectangular subdomains of dimensions
, with
. In such domain a wave with length
(i.e. the wave number is
) and amplitude
is imposed. Denoting the ratio
by
the following velocity potential can be considered:
valid for small values of
. In previous equations
is the angular frequency given by the dispersion relation of gravity waves:
, and
corresponds to the flat free surface (In Fig. 13 of Souto et all (2012)[1] it is wrong described)
Therefore the velocity field can be computed as
. It should be noticed that for
a flat free surface is obtained.
With such velocity potential, for a viscous fluid, it is possible to get an analytical solution for the kinetic energy decay[2]:
where the kinematic viscosity can be computed from the Reynolds number:
In our simulation
,
,
,
and
, where
is the initial distance between the particles.
Setting up the simulation
References
- ↑ 1.0 1.1 Antonio Souto-Iglesias, Fabricio Macià, Leo M. González, Jose L. Cercos-Pita. On the consistency of MPS. Computer Physics Communications, 2012
- ↑ J. Lighthill. Waves in Fluids. Cambridge University Press, 2001