OpenFOAM is supplied with its own mesh generator, blockMesh.

OpenFOAM applications handle unstructured meshes of mixed polyhedra with any number of faces: hexahedra, tetrahedra, degenerate cells, basically anything (see diagram).

Mesh generation is made simple by the fact that a cell is simply represented as a list of faces and a face as a list of vertices: this makes mesh handling very easy even for complex meshes with, say, embedded refinement or complex shapes near the boundary.