Some work on Fluid dynamics
Free moving boundaries:
To handle moving boundaries in some fluid flow problems you can apply the arbitrary Lagrangian-Eulerian (ALE ) formulation . The method covers situations in which the topology of the geometry does not change during the simulation and a suitable PDE for the mesh velocity exists.
In the video above is a model of a circular domain (radius 0.7) with a fluid about it. A "gravity like force" \(f_x=-10x, f_y=-10y\). keeps the fluid on top of the circular domain. The motion of the fluid is triggered by an initial velocity.
Sloshing Tank
The sloshing of fluid in a tank is a well-studied problem that has applications in a number of practical situations. The problem is relevant to
a) the safety of transporting fluids in tankers;
b) the automotive, aerospace and shipbuilding industries.
Fluid sloshing in road tankers may result in overturning of the vehicle, and resonant movement of fluid within ship cargo tanks is also of concern. The use of fluid-filled tanks is also used to act as dampers on the motion of city buildings in high winds.
The fluid motion is modeled with the incompressible Navier-Stokes equations. The fluid is initially at rest in a rectangular tank. The motion is driven by the gravity vector swinging back and forth, pointing up to 4 degrees away from the downward y direction at its extremes.
Some useful Link:
Cygwin installation under windows
http://www2.warwick.ac.uk/fac/sci/moac/currentstudents/peter_cock/cygwin/part2/
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