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arXiv · 2402.06199

A generalized formulation for gradient schemes in unstructured finite volume method

Mandeep Deka·Ashwani Assam·Ganesh Natarajan
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Abstract

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.

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Mandeep Deka, Ashwani Assam, Ganesh Natarajan. 2024-02-09. A generalized formulation for gradient schemes in unstructured finite volume method. https://arxiv.org/abs/2402.06199

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