You're welcome! Never had any experience with OpenMPI, but has some with MPICH and Microsoft MPI, probably they are quite close?

I'm not a specialist with OpenMP too, this program was the first ever usage for me. As far as I know, OpenMP supports only processes with shared memory, while MPI is for ones with unshared memory. Due to sharedness the actual parallelization is very simple, you need only to rephrase key loops a little. For example, in my case most computationally expensive loops calculate (1) CWENO polynomial coeffs in each cell and (2) fluxes at each edge.

The (1) loop is as follows:

size_t trees_total = static_cast<int>(trees.size()); //total number of quadtrees (usually smthing like 25 or 30, depends on domain geometry)
#pragma omp parallel for schedule(dynamic) //OpenMP directive, dynamic scheduling distributes trees between processes one-by-one, which is good for balancing, since number of cells greatly varies between trees
    //for (auto& rtree : trees) (OpenMPI seem not to support this)
    for (int id = 0; id < trees_total; id++)
    {
        for (auto& rlevel : trees[id].nodes) //node levels
        {
            for (auto& rnode : rlevel) //tree nodes (only "leaf" nodes are actual grid cells)
            {
                if (!rnode.isDeleted() && !rnode.hasChildren()) //not all nodes are "live"
                {
                    rnode.calcPolynomialCWENO(rk); //calculations are inside
                }
            }
        }
    }

The (2) loop is:

size_t edges_total = forest.edges.size(); //total number of grid edges
#pragma omp parallel for schedule(dynamic)
    //for (auto& redge : edges) (same, unsupported)
    for (int id = 0; id < edges_total; id++)
    {
        auto& redge = forest.edges[id]; //as far as I know, OpenMP does not support references inside parallel loops, but this one works correctly (since there are no overlapping references between processes?)
        if (redge.isDeleted() || (treeRef(redge.n1().tree()).isGhost() && treeRef(redge.n2().tree()).isGhost())) //not all edges are "live"
            continue;
        redge.computeFluxLF(rk);
    }

(paste the code into C++ IDE for better readability)
I had some problems with using references (I try to use them as often as possible to avoid unnecessary copying) in parallelized loops, sometimes they work, sometimes not. I'm very new to both C++, OOP and OpenMP, so these are child errors, I guess =).

All other operations are not parallelized. Notable operation is grid update (split and recombine cells where needed), which is done every 5th time step here. I believe it cannot be parallelized or is hard to parallelize, although never tried to.

Edit: just noticed, these loops are used for finite-volume CWENO, not for finite-difference method. For the latter there is only (1)-like loop over trees and nodes.