Modern multicore and manycore processors exhibit multiple levels of parallelism through a wide range of architectural features such as SIMD for data parallel execution or threads for core parallelism. The exploitation of multi-level parallelism is therefore crucial for achieving superior performance on current and future processors. This paper presents the performance tuning of a multiblock CFD solver on Intel SandyBridge and Haswell multicore CPUs and the Intel Xeon Phi Knights Corner coprocessor. Code optimisations have been applied on two computational kernels exhibiting different computational patterns: the update of flow variables and the evaluation of the Roe numerical fluxes. We discuss at great length the code transformations required for achieving efficient SIMD computations for both kernels across the selected devices including SIMD shuffles and transpositions for flux stencil computations and global memory transformations. Core parallelism is expressed through threading based on a number of domain decomposition techniques together with optimisations pertaining to alleviating NUMA effects found in multi-socket compute nodes. Results are correlated with the Roofline performance model in order to assert their efficiency for each distinct architecture. We report significant speedups for single thread execution across both kernels: 2-5X on the multicore CPUs and 14-23X on the Xeon Phi coprocessor. Computations at full node and chip concurrency deliver a factor of three speedup on the multicore processors and up to 24X on the Xeon Phi manycore coprocessor.