Experiment with explicit hybrid solver

[henry2004y]

This is the first experiment with an explicit hybrid solver in FLEKS. During the changes, I noticed that the current design always assumes species 0 to be electron. As a temporary workaround, we introduced a activeSpecies vector to keep track of active populations.

Summary of Changes

1. Hybrid Solver & Generalized Ohm's Law
   Implemented the full generalized Ohm's law: $$\mathbf{E} = -\mathbf{U}_i \times \mathbf{B} + \frac{\mathbf{J} \times \mathbf{B}}{n_e} + \eta\mathbf{J} + \frac{\nabla P_e}{n_e}$$

where:

$\mathbf{U}_i$: Ion bulk velocity (from particle moments)
$\mathbf{J} = \nabla \times \mathbf{B}$: Current density
$n_e \approx n_i$: Electron density (quasi-neutrality)
$P_e$: Electron pressure (adiabatic)
New Parameters:

• useHybridPIC (logical): Activates hybrid mode (disables Maxwell solver).
• etaResistivity (real): Resistivity $\eta$.
• electronTemperature, electronGamma, electronDensity0 (real): For adiabatic pressure gradient.
• nHallSubcycle (int): Number of subcycles for B-field update (Hall term stability).

2. Architecture Updates

• update_E_hybrid(): Computes the convection term $-\mathbf{U}_i \times \mathbf{B}$. This term depends on particle moments and is frozen during the B-field subcycling.
• update_B_hybrid(): New function that subcycles the B-field update. In each substep (dt_sub = dt/nHallSubcycle), it:
  • Recomputes $\mathbf{J} = \nabla \times \mathbf{B}$.
  • Computes B-dependent terms: Hall, Resistivity, and Pressure Gradient.
  • Updates $\mathbf{B}$ using the combined E-field.
• Particle Handling:
  • Electron Removal: When useHybridPIC is true, electron particles are not initialized or moved.
  • Active Species Refactor: Replaced raw nSpecies loops with activeSpecies vector iteration to efficiently handle cases where some species (electrons) are present in the config but active (null).

3. File Changes

• Pic.h: Added new parameters and update_B_hybrid declaration.
• Pic.cpp:
  • Implemented update_E_hybrid and update_B_hybrid.
  • Modified particle_mover and iterators to use activeSpecies.
  • Added parsing for #HYBRIDPIC, #RESISTIVITY, #ELECTRONTEMPERATURE, #HALLSUBCYCLE.
• Domain.cpp: Registered new commands.
• PARAM.XML: Updated XML schema for new commands.

Verification

Hybrid Mode Validation

• Test Case: test_hybrid (based on test16_2d, not included in this PR since it is in the SWMF git repository; this is quite annoying for development!)
• Configuration:
  • useHybridPIC = T
  • etaResistivity = 1.0
  • electronTemperature = 5.12e-4, gamma = 5/3
  • nHallSubcycle = 4
• Result: Stable simulation, correct parameter parsing, and physics terms active.

Regression Testing (Standard GM-PC)

Verified that standard GM-PC functionality is unaffected by running the following regression tests (all passed with 0 differences against reference):

• test16_2d (GM-PC 2D)
• test16_3d (GM-PC 3D)
• test17 (2D Alfven Wave)
• test18 (3D Reconnection)
• test23_2d (2D Fast Wave AMR)
• test23_3d (3D Fast Wave AMR)
• test25 (3D Light Wave AMR)