CFD Online Discussion Forums

Well...there's a lot of stuff and i really hope you have at least some knowledge of these things or it will be impossible to give a clear explanation of all in a single post.

1) To solve a general PDE you need to discretize it. What is meant for discretize is to select a set of points in your domain, somehow spaced and fitted on the boundaries of the domain. What you do in discretizing the equation is simply choosing to solve the equation only in these points and writing the equation for each of this points (in a way which depends on the method used to solve it). So you're going to have a set of n equations for n unknown values (one per each of the points).

What is usually meant for grid is the whole set of these points and the connectivity rule between them. Generally speaking you can also assume that a node is one of these points.

2) Meshing and grid generation means the same, that is the creation of the grid, the set of points mentioned above.

3) This question could mean that you don't even know what a PDE is. Roughly speaking, diffusion is the process by which heat is conducted in solids; in math it is equivalent to div(k grad(T)) where T is the temperature and k the conductivity.
Convection is tipical of fluids and is intended for the transport of something with the velocity of the medium; in math it is equivalent to div(r u T), with r the medium's density, u the medium's velocity and T the transported quantity.

4) When considering a grid (or mesh), connecting the neighbor nodes with straight lines will give you a set of polihedrons. They usually are tetrahedrons or hexaedrons. The mesh (or grid) is said a polymesh when it is not simply composed of tetrahedrons or hexaedrons but also of more complex polihedrons.

Polyhedral or tetrahedral grids are always unstructured grids because there is no obvious connectivity rule between a node and the neighbour ones. A structured grid is a grid in which for each node the neighbour ones are identified by switching an index. I can't be more clear. If you search some figures it will be much more clear.

5) If it's possible to write the Taylor series of the velocity field around a point, the first three terms are a pure translation, a pure deformation and a pure rotation. The rotation is simply half the curl of the velocity field.

The circulation is a quantity which is defined for a closed curve and is the integral of the velocity field along this curve. Thanks to the Stokes theorem it can be shown to be equal to the surface integral (on the surface enclosed by the curve) of the vorticity (2 times the rotation) component along the normal to the surface.

An unique definition of a vortex is still missing. A vortex is what is created at wing's tips but also the main component of the turbulence structure. A region of highly concentrated vorticity is a possible definition (but definitely not a complete one)