Lecture Timeline · PHY653B
Computational Plasma Simulation, the second half of the computational sequence. Nine chapters, each ending in a working solver and a number it has to reproduce.
| Chapter | Topics | Wiki pages |
|---|---|---|
| Ch 1 | Foundations: the closure problem, collision operators, normalisation, V&V, manufactured solutions, research craft | Closure problem · Collision operators · Normalisation & resolution · Verification & validation · MMS |
| Ch 2 | Vlasov dynamics: semi-Lagrangian solver, Landau damping, recurrence, trapping, conservation diagnostics | Vlasov–Poisson · Semi-Lagrangian solver · Landau damping numerically · Recurrence · Nonlinear trapping — 🔬 Vlasov widget |
| Ch 3 | PIC done properly: Monte-Carlo sampling, shape functions, Boris pusher, EM PIC, Weibel, how PIC lies | Shape functions · Boris pusher · Weibel instability · PIC noise & heating |
| Ch 4 | Numerical diagnostics: dispersion from data, growth rates, spectra, synthetic diagnostics, uncertainty | From arrays to claims · Growth-rate fitting |
| Ch 5 | Magnetohydrodynamics: seven waves, Godunov, Brio–Wu, the divergence constraint, Orszag–Tang, resistive MHD | Godunov MHD · Divergence constraint |
| Ch 6 | Gyrokinetics: the ordering, the gyro-average, ITG, drift-wave turbulence, zonal flows | Gyrokinetic ordering · Zonal flows |
| Ch 7 | Lattice Boltzmann I: where the lattice comes from, Chapman–Enskog, boundaries, stability | D2Q9 lattice · Chapman–Enskog — 🔬 LBM widget |
| Ch 8 | Lattice Boltzmann II: the thermal lattice, Boussinesq coupling, de Vahl Davis, Rayleigh–Bénard | Thermal LBM |
| Ch 9 | Lattice Boltzmann III: temperature-dependent transport, stability, validating without an exact solution | Variable transport |
🔬 = a live solver you can drive in the browser. See Simulations.
The benchmark ladder
Each chapter's deliverable is a number, not a picture:
| Chapter | The number your code must reproduce |
|---|---|
| 2 | \(\gamma = -0.15336\) at \(k\lambda_D = 0.5\); recurrence at \(T_R = 2\pi/(k\Delta v)\) |
| 3 | Weibel linear growth rate; second-order convergence of the Boris pusher |
| 4 | The dispersion relation, recovered from raw field data |
| 5 | Brio–Wu wave positions; \(\nabla\cdot\mathbf{B}\) at round-off |
| 7 | \(\nu = c_s^2(\tau - \tfrac12)\), verified against a fitted Poiseuille parabola |
| 8 | de Vahl Davis Nusselt numbers; \(Ra_c = 1707.76\) |
| 9 | Recovery of the constant-\(\nu\) limit; observed order via MMS |
Read Chapter 1 twice
It looks like preamble and it is the foundation. By Chapter 9 there is no benchmark left to hide behind, and the only thing standing between your result and a plausible-looking fabrication is the verification apparatus set up in the first chapter.