Fluid Dynamics Without Fluids

This chapter will discuss some interesting real applications where Fluid Dynamics equations found fruitful appliances without dealing with "strictly speaking" fluids. In particular, thanks to the large set of analyses performed over different kinds of fluids in different operating and boundary conditions, a wide range of Computational Fluid Dynamics algorithms flourished tackling different aspects, from convergence rate, to stability according to the discretization, to multigrid and linearization problems. This robust and thorough background, both on the- oretical and on practical aspects, made Computational Fluid Dynamics (CFD) appealing also to other sciences and applications where Fluid Dynamics equations, or similar equations very close to them, can be useful in describing complex phenomena not related to fluids. Some applications that will be discussed concern, e.g., Geometry of liquid snowflakes whose con- tour is growing steered by curvature, staring from a circle. Furthermore Image Restoration and Segmentation can also benefit from CFD since a set of evolutionary algorithms, based on level-set curvature flow equations, plays a fundamental role in steering active contours or snakes through the noise present in the image till the complete warping of the desired framed object. Also in this case advanced techniques like Ghost Fluids Method for two competing fluids dynamics can be used to separate different objects in images. Other interesting appli- cations that will be described concern applicability of CFD to surface extraction from cloud of points. This is a common problem when complex clouds of points, representing 3D objects or scenes are obtained by laser scanners or multi-camera vision systems. These points represent unambiguous features from corners or sharp edges and the final 3D closed surface must fit on these points smoothly interpolating empty space between them. Also in this case CFD can provide useful tools to define the evolution of a 3D surface representing the border between two competing fluids, one representing the "inside" and the other the "outside" of the object itself. The two fluids evolution will stop when surface sticks on all the 3D points: the viscosity of the two fluids will control the smoothness of this surface that will wrap the cloud and tur- bulence is used to model injection into grooves or narrow holes. This chapter will also discuss another interesting application of CFD to robotic navigation in complex environments where we are looking for the best path, both in terms of length and distance from objects, through a set of obstacles, different terrains traversability or path slope. Also in this case an imaginary fluid with a predefined viscosity floods from the robot position through the whole environ- ment, its front evolution speed, accordingly to CFD, will be slower in narrow passages and, once it reaches the target, it will define the easiest way.