The Euler Eigensystem in an Arbitrary Direction — Three Waves, Two Repeats, One Singularity
·5 min read
Where the left eigenvector breaks when n̂ tilts, and the three conventions that dodge it
Saving Gradients on Unstructured Grids — Moving Least-Squares Approximation
·5 min read
A local polynomial fit that recovers both values and derivatives from scattered points
The Star That Started Moving — Well-Balanced FVM and Angular Momentum in Polar Coordinates
·5 min read
Mis-discretize 2P/r and a quiet star will leak gas out of its center.
Skewed Cells Bend Gradients — Green–Gauss vs Least-Squares Reconstruction
·5 min read
Two ways to compute ∇p on unstructured meshes, and how their accuracy diverges
FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques
·6 min read
A comparison of the mathematical origins, pros and cons, and best application areas for the Finite Difference Method (FDM), Finite Element Method (FEM), and Finite Volume Method (FVM).