A PVS is not what you want for this type of application—it is good for indoor environments but very unsuitable for outdoor environments, especially in light of its shortcomings when dealing with dynamic objects and addition to better structures available that handle both dynamic objects and specifically terrain much much better.

Updating a PVS in real-time is not practice, so you would not be putting dynamic objects into it. Meaning only the terrain and buildings would be relevant choices, and both can be done better.

Terrain should be rendered using either GeoMipmaps or GeoClipmaps. GeoClipmaps is the fastest but takes some work to implement.

After that, the rest of the world should be subdivided into an octree or a hybrid between an octree and a quadtree (my suggestion). This will handle all the static objects besides the terrain as well as dynamic objects inside the game world. Standard frustum culling would be applied here.

Then PVS’s would only be applied to the interiors of buildings.

There is no one-fits-all solution to a game world. Each part is best served by a specific structure or algorithm.

L. Spiro

The PVS algorithm in the OP won't work. It's easy to imagine a case where, with the camera at he centre of cell 'A', you can't see cell 'B' at all, but with the camera near the edge of cell 'A' you can.
The chance of these errors occurring is proportional to your cell size. To be error free, you need infinitely small cells!

Most precomputed PVS systems will use the world geometry to define the empty/movable space, and then decompose these empty spaces into a set of polytopes (convex shapes). The faces that are shared between two polytopes become portals. For each "sector" (polytope), for each portal, you can then construct a frustum of the potentially visible area through that portal. You can then step into the adjacent 'sector', and recursively apply the same process, but ignoring any portals outside of this frustum, and when stepping through the next portal, you use the union of the current frustum and the new frustum (basically clipping so, when looking from sector A to B to C, you only check for what's inside the A->B frustum AND inside the B->C frustum).

It sounds a bit simpler if you describe it with planes (instead of frustra like I did), and draw it out in 2D.

e.g. here's a top-down view of a level with one room connected to two corridors. The level has been compiled into a BSP-tree, which is binary tree (each node has two children) where each node defines a plane that splits the world in half.

Originally, Quake1 chose to use BSP trees because they allow you to quickly sort your polygons from back-to-front, so they could render without a z-buffer! However, they turned out to be pretty useful besides that, and many indoor renderers still use them.

Each of the red lines in the picture is a plane from the BSP tree. The letters are then the sectors that are formed after the world has been split by these planes.

If we want to build the PVS for sector A, first we add A to the list (A can see A ), then we iterate through it's portals (planes). It's only got one portal in this example, which leads to B. We add B to the list, because it's directly connected via this portal, so it's obviously visible. Now we iterate through B's portals -- it has one to D and one to C. We check each of those portals against the planes we've already crossed -- so far we've only crossed from A into B. The portal from B to D is behind (or parallel with) the portal from A to B, so we can skip it! The portal from B to C is in front of our plane, so we add C to our visible list.

In the diagram, C has no further portals, but if it did, we'd check that they were in front of the A->B plane, and in front of the B->C plane.

Speaking of Quake 1, it's worth noting that it also used it's PVS for reducing client/server communication (only potentially visible entities need be sent) and for visibility tests in combat. That's something you might want to consider and which could influence your choice of what technique you use for this.