Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Award: G5472561672
OpenAlex ID: W4391766560