why is it that hexahedral meshes are more accurate that tetrahedral meshes while still having a lower cell count. Why are they more preferred, i am a beginner to cfd and anybody who could explain this to me in simple term is greatly appreciated.
Expanding on Pascal's comment ... hex (or quad) meshes generally work better (i.e., more accurate) for wall-bounded flows since we can maintain orthogonal grids in the wall-normal direction. This is a consequence of the better accuracy of the hex elements since the angle between faces can be kept close to 90-degrees. When the Reynolds number is high, we need very fine spacing in the wall-normal direction. Hex grids allow very fine wall-normal spacing but without large face skewness. Prism element can also help with this but they aren't used as commonly.
And aside from "numerical" efficiency, there is also a "computational" efficiency factor. Structured grids with hex or quad meshes (either regular or curvilinear) can be implemented a bit easier and usually execute quite a bit faster than algorithms that support unstructured (usually with tets but can be a blend of tets, prisms, and hexs). This is because of the implicit topology of the structured grid. That is, you can implicitly know the neighboring cells and faces. With unstructured mesh algorithms, you have to look up the connectivity between cells (and edges and faces) from a table which can be costly on the computer.
I see at least two point of views: from the physics view point, and from the numerical analysis view point:
1) Physics: very often, flows are what I would call "directional", be it e.g. the flow of a river or a flow around an airfoil, or in a pipe (look up in the internet for images representing these flows). And then it seems physicaly sensible to have mesh faces in 3D (or edges in 2D) that follow the flow direction, which is achieved by the lateral faces of hexahedra (quadrangles in 2D), while tetrahedra (triangles in 2D) necessarily have faces that cross the flow.
2) Numerical analysis: when one performs rigourous error estimations between computed and exact solutions, in many cases the angles of the mesh cells come into play in the evaluation of these errors through a 1/sin(theta) in the estimation, where theta is the minimum angle of the cell (or in some cases the maximum angle), and so in hexa or rectangles, if they are not too distorted, you often have theta close to pi/2, even if the cell is very elongated in one direction, which is optimal because then 1/sin(theta) is close to 1; whereas in tetra or triangles, especialy if the cell is elongated, theta may be closer to zero (or the max angle closer to pi), and then 1/sin(theta) may be much higher than one, which spoils your error estimate. An additional point is that some schemes have superconvergence properties on (uniform) hexa / rectangles: they converge one order faster (e.g. in h^2 instead of h, where h is the mesh typical length) than on tetra / triangles.
Expanding on Pascal's comment ... hex (or quad) meshes generally work better (i.e., more accurate) for wall-bounded flows since we can maintain orthogonal grids in the wall-normal direction. This is a consequence of the better accuracy of the hex elements since the angle between faces can be kept close to 90-degrees. When the Reynolds number is high, we need very fine spacing in the wall-normal direction. Hex grids allow very fine wall-normal spacing but without large face skewness. Prism element can also help with this but they aren't used as commonly.
And aside from "numerical" efficiency, there is also a "computational" efficiency factor. Structured grids with hex or quad meshes (either regular or curvilinear) can be implemented a bit easier and usually execute quite a bit faster than algorithms that support unstructured (usually with tets but can be a blend of tets, prisms, and hexs). This is because of the implicit topology of the structured grid. That is, you can implicitly know the neighboring cells and faces. With unstructured mesh algorithms, you have to look up the connectivity between cells (and edges and faces) from a table which can be costly on the computer.
To align the flux vectors with the normal faces (or edges in 2D) is a well-know practice that avoid the issues that Pascal has commented.
Tetra grids are very flexible and faster to meshing. With with little steps a good mesh can be generate. But is hard to control all mesh parameters, mainly in complex geometries. And obey the solver recommendations as min and max angles, quality, volume ratio, 2x2 and 3x3 determinant, skewness, orthogonality, etc. Each solver or code has its good recommendations to these parameters.
Hexa grids, is very fine and elegant, but require a better mesh generation skill. It almost a sculpture method with the mesh blocks. But as our friends have cited. It is easy to control the spacement, inflation ratio and the geometric parameters and to align the normal face elements to the flow lines.
It is possible use tetra meshes with prismatic elements next to walls in some inflation layers. It is used extensively in ANSYS CFX and Fluent codes for example. What will give a good performance in the boundary layers region. regarding to this, the model recommendations to maseh spacement must be respect as y+ value.
A hexa mesh can be unstructured. In few words ( there are some math implications) pends on the elements indexing, e.g. if you can index in an organized and sequential way the mesh will be structured,whether is formed by triangles or quads, tetra or hexas. Of course, it is practically impossible to do it in a 3D complex tetra mesh. Once again, as pointed out Christopher, it will dependent of the code design. I avoid to use the term unstructured as synonymous of tetra meshes. But is common.
The geometrical anisotropy( distortions in size and angles and aspect ratios) will impact on the coefficients of your matrix and its conditioning. The consequence is a bad conditioned system and convergence issues.
Other point is regarding to the formulation: cell-center or cell-vertex. in cell-vertex the element it will be the volume of control, hence, we have a 1:1 ratio of elements and volumes of control in both meshes. In cell-vertex this ratio is 4:1 in tetra and ~1:1 in hexa meshes. E.g. 1M of elements in cell vertex implies in 250K volumes of control in tetra elements or ~1M of V.C. in hexa elements. This is one difference between Fluent and CFX, the 1st is cell-center, and the 2nd one is cell-vertex
Solvers today are generally better at giving good accuracy on tet meshes than they used to be a couple of years ago. Moreover, in a complex geometry it can be more difficult to create a conforming hex mesh leading to worse mesh quality and difficulties to converge the pressure solver. But if the geometry allows for it, conforming hex has advantages as has been outlined above.
And if one would like to do mesh refinements studies it's of course also much more consistent.