Physics / advanced
Numerical experiments in classical physics
Design verifiable simulations of mechanics, waves, fluids, and fields, using convergence, conservation, stability, and model validation as explicit standards.
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Module 01 advanced
Numerical experiments in classical physics
Design verifiable simulations of mechanics, waves, fluids, and fields, using convergence, conservation, stability, and model validation as explicit standards.
- 01
Nondimensionalizing a physical simulation
Choose reference scales, preserve dimensionless physical ratios and translate numerical tolerances consistently.
32 min - 02
Symplectic integrators for orbital motion
Preserve Hamiltonian geometry while assessing energy, phase and close-encounter errors separately.
32 min - 03
Adaptive time stepping and event detection
Control a local error estimate while separately resolving stability and the time of physical events.
32 min - 04
N-body force calculation and softening
Separate pair-force symmetry, approximation error and the physical bias introduced by gravitational softening.
32 min - 05
Finite-difference wave propagation and CFL
Derive a centered wave update, initialize it consistently and identify its particular stability and dispersion limits.
32 min - 06
Finite-volume fluxes and conservation
Update cell averages with one shared interface flux and distinguish conservation from stability and entropy selection.
32 min - 07
Particle-in-cell plasma discretization
Connect particle deposition, grid fields and interpolation without confusing global charge balance with local discrete continuity.
32 min - 08
Electrostatic Poisson solvers and boundaries
Solve a tiny Dirichlet system and identify the compatibility and gauge constraints of periodic or Neumann electrostatics.
32 min - 09
Spectral fluid methods and aliasing
Recognize nonlinear mode folding and distinguish a dealiased finite computation from continuum fluid claims.
32 min - 10
Verification, validation and discretization error
Estimate numerical convergence without turning it into a claim that a physical model is experimentally validated.
32 min