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.
Skew the Element 45° and the Stiffness Grows 2.5x — Metric Tensors and Constitutive Tensor Transformation
·8 min read
In curvilinear coordinates, writing strain as covariant components means the constitutive tensor has to move too. Skip that step and every skewed element reports the wrong stiffness.
Wrapping a Rectangular Grid Around a Wing — Curvilinear Coordinate Transforms and Grid Metrics
·6 min read
On a wavy mesh the Jacobian runs from 0.62 to 1.38 and stays positive. Write the flux as y_η and the freestream residual falls to about 1e-16.
The Star That Started Moving — Well-Balanced FVM and Angular Momentum in Polar Coordinates
·6 min read
Mis-discretize 2P/r and a quiet star will leak gas out of its center.