numerical-methods
7 parts · sequential reading recommended
- 01
FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques
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).
Mar 9, 2026
- 02
Discontinuous Galerkin Method (DGM): High-Precision Discretization for Unstructured Grid Compressible Flow Analysis
Step-by-step summary from DGM weak form derivation to Gauss quadrature and unstructured grid implementation.
Apr 20, 2026
- 03
Choosing a CFD Linear Solver: Comparing Convergence Speeds from Jacobi to BiCGSTAB
Comparing the characteristics and convergence speeds of the four major Krylov subspace solvers with code and simulation.
Apr 22, 2026
- 04
When Lax–Wendroff Shook at a Step — Building a 2nd-Order TVD Advection Scheme with Flux Limiters
Sidestep Godunov's theorem to build a monotone 2nd-order advection scheme
Apr 24, 2026
- 05
[Paper Review] When WENO Smears Small Eddies — Fu (2019) Low-Dissipation TENO Finite-Volume Scheme
Why 5th-order WENO-JS still smears smooth scales, and how TENO's sharp cutoff fixes it
Apr 25, 2026
- 06
[Paper Review] Beating the Storm Clock — Casulli–Walters (2000) Semi-Implicit Shallow Water on Unstructured Orthogonal Grids
A shallow-water algorithm that stays stable at large time steps
Apr 26, 2026
- 07
[Paper Review] Pick the Reconstruction with Smaller Jumps — Deng (2018) MUSCL-THINC-BVD
Choosing between two candidate reconstructions by minimizing total boundary variation
May 2, 2026