Simulations
These are not animations of results computed elsewhere. Both widgets are real solvers running in your browser — the same schemes described in the notes, at reduced resolution — and both are checked against the exact answers the course insists on.
Live
- Vlasov–Poisson Landau damping — a semi-Lagrangian solver with Strang splitting and cubic interpolation, on a 64 × 256 phase-space grid. Measures its own damping rate and lands within a few tenths of a percent of the exact root \(\gamma = -0.15336\), then shows you recurrence arriving on schedule.
- Lattice Boltzmann D2Q9 — a BGK solver with Guo forcing and halfway bounce-back. Fits the channel profile and recovers \(\nu = c_s^2(\tau - \tfrac12)\) to under 1% across the useful range of \(\tau\); switch cases for a von Kármán street.
What they are verified against
| Widget | Benchmark | Tolerance achieved |
|---|---|---|
| Vlasov | exact Landau roots at \(k\lambda_D\) = 0.3–0.6 | γ within 0.3–4%, \(\omega_r\) within 0.2% |
| Vlasov | particle number conservation | 1 part in \(10^8\) |
| Vlasov | recurrence at \(T_R = 2\pi/(k\Delta v)\) | within 2–5% |
| LBM | D2Q9 moment conditions | machine precision |
| LBM | \(\nu = c_s^2(\tau - \tfrac12)\) | 0.1–1.2% |
| LBM | mass conservation | 3 parts in \(10^{13}\) |
That table is the point of the course in miniature. Every one of those numbers was known before the code was written, which is what made it possible to tell whether the code worked.
Reduced resolution is still a real simulation
These run at grid sizes chosen so your laptop keeps 60 fps, which is roughly an order of magnitude coarser than a production run. Everything they demonstrate is genuine; what they cannot show is the regime where resolution itself becomes the physics — filamentation below \(\Delta v\), or the high-\(Re\) limit where LBM stability fails. Those are on the problem sets.
Related tools in the wiki family
The prerequisite course PHY653 has the integrator-comparison arena; PC368 has a Boris-pusher drift-orbit lab and a cold-plasma wave explorer that solve the analytic theory these codes are checked against.