The Numerics Lab
Numerical methods from the implementation point of view.
The Numerics Lab focuses on implementation notes, CFD discretization experiments, small programs, solver prototypes, and reproducible examples.
Examples are developed as small, readable programs and published in the public repository: iAmKonio/the-numerics-lab.
More finite element examples will be added over time. FEM is one of the areas where I have implemented numerical methods in code, so this section will grow from Poisson and diffusion foundations toward advection-diffusion and stabilized convection examples.
Finite Difference Methods
Grid-based derivative approximations, advection/diffusion examples, stability, CFL, boundary conditions, and explicit/implicit time stepping.
Finite Volume Methods
Conservation laws, control volumes and face fluxes, upwind/central/MUSCL-style reconstruction, with planned pressure–velocity coupling.
Finite Element Methods
Weak forms, basis/shape functions, element matrices, assembly, boundary conditions, and Poisson/diffusion starters.
Weak and strong DG forms, numerical fluxes, nodal/modal bases, quadrature, conservation/stability tests, and DGSEM orientation.
Lattice Boltzmann Methods
D2Q9 model, collision and streaming, BGK relaxation, boundary conditions, and simple channel/lid-driven cavity examples later.