feat(vfp2d): couple ion hydro and kinetic-electron pressure

[joglekara]

Summary

• add the Gate 0a standalone 2D ideal-ion MUSCL-HLLC finite-volume backbone
• close Gate 0b with quantitative Riemann, translating-vortex, Sedov, and magnetic-divergence benchmarks
• add Gate 1 ion-frame electron operators for bulk transport, deformation, frame acceleration, and local finite-mass exchange
• add the Gate 2a/2b ion-kinetic split with finite-mass remapping, full kinetic electron-pressure feedback, and sparse high-harmonic deformation operators
• close the nonlinear coupled-energy gate under timestep and spatial/radial refinement

Nonlinear energy gate

The coupled map is now the symmetric composition

1. ion hydro half-step;
2. coupled pressure/exchange half-step;
3. full kinetic-electron step at midpoint ion kinematics;
4. coupled pressure/exchange half-step; and
5. ion hydro half-step.

The kinetic-Ohm Ampere projection changes only f1, but in a moving ion frame that changes lab-frame electron energy by u_i . Delta p_e. Runs now accumulate that projection work explicitly and save both total_energy and accounted_total_energy = total_energy - current_projection_energy. A direct unit test compares the ledger to the independently measured lab-frame energy jump.

The nonlinear periodic benchmark evolves nonuniform electron density and temperature, accelerates the ions through the full f0 + f2 electron pressure, and generates magnetic field. Its declared accounted-energy tolerance is 3.1e-9:

• the tolerance is met for dt = 2e-3, 1e-3, 5e-4;
• ion-velocity and magnetic observables converge above order 1.8 in time;
• the energy defect decreases by more than 8x from nv = 24 to nv = 96; and
• the energy defect decreases by more than 8x from nx = 6 to nx = 12.

Gate 0b benchmarks

• Sod and pressure-ratio 1e5 strong-shock tubes are compared with an exact Euler Riemann solution on both coordinate axes; normalized L1 tolerances are 3.5% and 12%, respectively.
• A translating isentropic vortex converges above order 1.7 from 24x24 to 48x48.
• A Cartesian Sedov blast preserves total energy to roundoff, stays positive and transpose-symmetric, and keeps fourfold kinetic-shell anisotropy below 5%.
• A divergence-free magnetic field remains divergence-free through 24 nontrivial Faraday updates to 2e-12 absolute tolerance.

Physics demonstrated

• exact frozen-ion regression to the kinetic-Ohm solver when u_i = 0
• analytic ideal bulk magnetic advection with no magnetic-divergence source
• finite-mass velocity-frame translation preserving electron density and lab-frame momentum/energy to roundoff
• symmetric momentum, temperature, and electron-pressure exchange preserving coupled lab-frame invariants
• scalar f0 plus traceless f2 electron pressure and equal-and-opposite pressure work
• classical local-Maxwellian Biermann generation with spectral convergence
• Epperlein-Haines Z* response recovering the analytic Spitzer-Harm T^(5/2) heat-flux coefficient
• Galilean, compression, shear/f2, rigid-rotation, and accelerating-frame checks

Explicit boundary

This remains a draft and is not ready for production parameter scans. Moving-ion production is still periodic, nonrelativistic, unsharded, kinetic-Ohm, and quasineutral. ElectronIonExchange remains a weak-drift moment model rather than a full finite-mass Landau operator. Nonperiodic coupled boundaries and production-scale validation remain future gates.

Verification

• uv run pytest -q tests/test_vfp2d -- 66 passed
• uvx ruff check on all touched solver and test files -- passed
• uvx ruff format on all touched solver and test files -- passed
• git diff --cached --check -- passed

The earlier repository-wide non-slow run was interrupted after 7 passing tests because the existing test_reuse_config_dict path remained in urllib3 network retry for four minutes. The complete relevant VFP2D suite is green.