2024/02/09 by Deka, Mandeep, Assam, Ashwani, Natarajan, Ganesh
#65N08 #76M12 #F.0 #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #G.1.8 #G.4 #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2402.06199
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.