By default, the density is unity and the molecular viscosity is zero (i.e. there is no explicit viscous term in the momentum equation). In practice, it does not mean that there is no viscosity at all however, because any discretisation scheme always has some numerical viscosity. Of course, the lower the numerical viscosity, the better. Gerris has quite good properties in this respect.
This is perfectly right in the case of flow around smooth solid boundaries. If there is a sharp corner (as for the half-cylinder), the potential flow solution is singular in the sense that the velocity tends to infinity as one gets closer to the corner. In practice (finite difference numerical solution) and in reality, the local numerical (or real) viscosity near the corner, smears out the singularity, which results in the creation of a (point) source of vorticity which is then carried away by the mean flow (as you can see on the half-cylinder example).
Even in the case of a smooth geometry, numerical inaccuracies in the boundary conditions on the solid surface can lead to the generation of a small amount of vorticity (much smaller than what is generated at a discontinuity though).
It is possible to change the size of the unit GfsBox, however, I would encourage you to think in ``relative units'' rather than ``absolute units''. When studying fluid mechanics (and other physical) problems it is almost always a good idea to use non-dimensional units. This makes relevant independent parameters (such as the Reynolds number for example) immediately apparent. When using Gerris I would recommend scaling all your physical input parameters by a reference length (the physical length of the GfsBox). This also eliminates the need for changing the length of the GfsBox.
You would have to non-dimensionalise both the model ship geometry and wind speed.
The reference length of the GfsBox would be
3*150 meters
You might want to use the transform program to do
that, something like this:
You also have to keep in mind that the bottom boundary of a 3D box is
at z = - 0.5
However, keep in mind that the only relevant parameter for the
(constant density) Navier-Stokes equations is the Reynolds number. If
you do not include any explicit viscous term the (theoretical)
Reynolds number is always infinite. In practice this means that the
inflow velocity has only a uniform scaling influence on the final
solution. For example
Let's say your reference scale is
L = 450 meters
You thus need to multiply both t and dt by T = 9 sec
The units of vorticity are
Not really if what you mean is a constant density throughout the
domain. In the case of the incompressible constant-density Navier-Stokes
equations, the density is irrelevant. It is only a scaling factor for
the pressure.
What this really means is that Gerris can deal with flows where
the density varies across the domain (e.g. a mixture of two miscible
fluids, or density variations due to salinity variations in the sea for
example).
The code is indeed not perfectly numerically symmetrical. This is due
mainly to the tolerance in the solution for the pressure equation, if
you decrease the tolerance you should see smaller
asymmetries. You can do this using
Your question is interesting, it comes down to the meaning of
``pressure'' for incompressible flows.
For compressible flows ``pressure'' has a thermodynamic definition
and is directly linked to other physical quantities through an
equation of state. It is defined on an absolute scale.
For incompressible flows ``pressure'' does not have a thermodynamic
definition (there is no equation of state linking it to other physical
quantities), rather it comes about as the stress field necessary to
enforce the incompressibility condition. In this context, only its
gradients are relevant, not its absolute value i.e. one can add any
constant to the pressure field without changing the solution.
Conclusion: If you don't like negative pressures just add any constant
necessary to make them positive.
% transform --scale 2.22222e-3 < model.gts > model_scaled.gts
How would I redimensionalise U,V,W and P?
then, the velocity field of simulation 1 at time t is exactly equal
(to machine precision) to the velocity field for simulation 2 at time
t/2.0
It looks like t and dt output by GfsOutputTime are also scaled? How would I scale t and dt to time in seconds?
How do I scale Vorticity?
T-1
The code provides support for the variable density incompressible Euler
equations. Does that mean you can input the density of the fluid density
(air, water, etc...)?
Although the initialised problem is symmetric, the solution
becomes asymmetric as time passes, why?
ApproxProjectionParams {
tolerance = 1e-6
}
ProjectionParams {
tolerance = 1e-6
}
How do I deal with negative values of the pressure?
Subsections
Next: Representation of solid boundaries
Up: The Gerris FAQ
Previous: Installation and coding
Contents