I Gave Curved Cells Their True Area and ∂x/∂x Stopped Being 1 — Why the Diagonal Cross-Product Area Fits Green–Gauss
·7 min read
Cell-center Jacobian volumes make ∂x/∂x miss 1 on a wavy FVM grid. The diagonal cross product matches straight faces, so a linear field stays exact.
When Gradients Go Wrong on Skewed Meshes — Green–Gauss vs. Weighted Least-Squares Reconstruction
·6 min read
On a flat cell, Green–Gauss can swing the gradient nearly sideways. Distance-weighted least squares cuts the curved-field error from 0.0293 to 0.0222.
Saving Gradients on Unstructured Grids — Moving Least-Squares Approximation
·6 min read
With h=0.07, order 2 and 25 scattered points, the Taylor MLS derivative of sin(2πx) has RMSE 0.21, about 3% of the 2π amplitude.