Parallel Block-Structured class abstraction for FDM-- Ideas

Not sure what you are asking. Do you want a global i,j,k system comprising all of the blocks. Why bother with that since each block has its own I,J,K system. Just store the data needed to satisfy the transfer of data to/from the layer(s) of ghost cells around each block. For parallelism, you need some form of load balancing algorithm designed to deal with multi-block grid systems. Those have been around for more than 30 years if you check the literature. You could have a global field class that has an an array of a structured grid classes as a component. NASAs CFL3D code is an example of what was at one time the state of the art in structured multi-block CFD codes (GitHub - nasa/CFL3D). Most general use CFD codes have moved to unstructured grids although there are still some applications where structured grid codes can be more accurate (and faster running). Given the speed of current HPC systems and the overall robustness of the underlying solver technology, grid generation is still the major bottleneck in terms of time to solution for a typical CFD analysis workflow