Currently, as a Ph.D. student, I am developing the HPC2, a fully portable, algebra-based framework capable of heterogeneous computing with many potential applications in the fields of computational physics and mathematics. This framework aims to provide a user-friendly environment suitable for writing numerical algorithms in terms of portable algebraic kernels. In its application to CFD, the algorithm of the time-integration phase relies on a reduced set of only three kernels: the sparse matrix-vector product, the vector element-wise operator, and the vector reduction. This algebraic approach combined with a multilevel MPI + OpenMP + OpenCL + CUDA parallelization naturally provides portability.