A generalized formulation for gradient schemes in unstructured finite volume method
<|reference_start|>A generalized formulation for gradient schemes in unstructured finite volume method: We present a generic framework for gradient reconstruction schemes on unstructured meshes using the notion of a dyadic sum-vector product. The proposed formulation reconstructs centroidal gradients of a scalar from its directional derivatives along specific directions in a suitably defined neighbourhood. We show that existing gradient reconstruction schemes can be encompassed within this framework by a suitable choice of the geometric vectors that define the dyadic sum tensor. The proposed framework also allows us to re-interpret certain hybrid schemes, which might not be derivable through traditional routes. Additionally, a generalization of flexible gradient schemes is proposed that can be employed to enhance the robustness of consistent gradient schemes without compromising on the accuracy of the computed gradients.<|reference_end|>
@article{deka2024a,
    title={A generalized formulation for gradient schemes in unstructured finite
  volume method},
    author={Mandeep Deka, Ashwani Assam, Ganesh Natarajan},
    journal={arXiv preprint arXiv:2402.06199},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.06199},
    primaryClass={math.NA cs.NA math-ph math.MP physics.flu-dyn}
}