We present the Circular Incident Edge Lists (CIEL), a new data structure and a high-performance algorithm for generating a series of iso-surfaces in a highly unstructured grid. Slicing-based volume rendering is also considered. The CIEL data structure represents all the combinatorial information of the grid, making it possible to optimize the classical propagation from local minima paradigm. The usual geometric structures are replaced by a more efficient combinatorial structure. An active edges list is maintained, and iteratively propagated from an iso-surface to the next one in a very efficient way. The intersected cells incident to each active edge are retrieved, and the intersection polygons are generated by circulating around their facets. This latter feature enables arbitrary irregular cells to be treated, such as those encountered in certain computational fluid dynamics (CFD) simulations. Since the CIEL data structure solely depends on the connections between the cells, it is possible to take into account dynamic changes in the geometry of the mesh and in property values, which only requires the sorted extrema list to be updated. Experiments have shown that our approach is significantly faster than classical methods. The major drawback of our method is its memory consumption, higher than most classical methods. However, experimental results show that it stays within a practical range.