Hardware-aware design and optimization is crucial in exploiting emerging architectures for PDE-based computational fluid dynamics applications. In this work, we study optimizations aimed at acceleration of OpenFOAM-based applications on emerging hybrid heterogeneous platforms. OpenFOAM uses MPI to provide parallel multi-processor functionality, which scales well on homogeneous systems but does not fully utilize the potential per-node performance on hybrid heterogeneous platforms. In our study, we use two OpenFOAM applications, icoFoam and laplacianFoam, both based on Krylov iterative methods. We propose a number of optimizations of the dominant kernel of the Krylov solver, aimed at acceleration of the overall execution of the applications on modern GPU-accelerated heterogeneous platforms. Experimental results show that the proposed hybrid implementation significantly outperforms the state-of-the-art implementation.