We present in this paper a discrete-ordinates transport method to perform 3D PWR transport simulations. The numerical technique takes profit of the Cartesian modular construction of the PWR geometry. The spatial mesh of the proposed method is composed of Heterogeneous Cartesian Cells (HCC). HCCs are basic geometrical patterns delimited by a box and having an arbitrary number of locally-extruded heterogeneous regions. The source is spatially expanded by piece-wise linear approximation in each region. The faces of the box, composing the boundary of the HCC, are discretized with a uniform Cartesian mesh. This surface sub-mesh is the support of a piece-wise linear representation of the interface angular flux. The linear expansion of the sources allows for a considerable reduction of the number of regions. Because of the Cartesian nature of the geometry, the method uses the effective spatial sweeping based on progression by front. Results on three-dimensional core simulations show accurate power distribution while minimizing the number of degrees of freedom. Since parallel computing is mandatory to access high-fidelity flux distributions in a reasonable amount of time, a domain decomposition algorithm is applied at each power iteration. Also, because of the slow convergence of the parallel block-Jacobi iterations, outer power iterations are accelerated by the Coarse-Mesh Finite Difference method (CMFD). In the present work, both transport and outer CMFD share the same domain splitting configuration and perform local multigroup source iterations to stabilize the scattering source. This allows for non-intrusive coarse-grained hybrid parallelism based on MPI/OpenMP directives. A set of 3D benchmarks will be proposed to access the accuracy and the parallel efficiency of the implementation.