RZ: conserve charge and current under binomial filtering

[clarkse-he]

Summary

The bilinear filter smooths rho and J as densities with an index-space stencil. On the unequal cell volumes of radial geometry (RZ / RCYLINDER / RSPHERE) this does not conserve the volume integral: charge and current are created or destroyed by every filter pass, with the bias concentrated near the axis where adjacent cells differ in volume by O(1) factors.

A naive extensive-quantity variant (filter rho*V, divide V back out) is conservative but wrong in the other direction: the index-symmetric stencil moves a quarter of the first ring's (large) charge into the (small) axis cells, spiking the axis density by more than 2x in our tests.

This PR applies the binomial passes to conserved densities in flux form: each pass is the divergence of a two-point diffusive flux with face-averaged volume factors, using the same volume conventions as the inverse-volume-scaling routines. This

• conserves the volume integral of rho and J exactly in the interior,
• leaves constant fields untouched,
• reduces to the standard (1/4, 1/2, 1/4) stencil where volumes are uniform (Cartesian behavior unchanged),
• passes zero flux through the axis face by construction (no below-axis guard dependence and no azimuthal-mode parity bookkeeping), and
• passes zero flux through non-periodic domain boundaries, so nothing leaks into guard cells that are never folded back.

WarpX::ApplyFilterJ dispatches current-density filtering to the flux form in radial geometries and to ApplyFilterMF elsewhere; ApplyFilterandSumBoundaryRho uses the flux form for rho in radial geometries. Field smoothing (gather field, fluid velocities, temperature diagnostics) intentionally keeps the plain stencil: those are not conserved densities.

Validation

On an RZ uniform-plasma deck with charge-weighted diagnostics (single filter pass on identical deposits, filtered vs unfiltered):

• near-axis rows are unbiased after filtering (ratios 0.99-1.00; the previous behavior distorted them),
• the filtered/unfiltered total-charge ratio is a one-time redistribution bounded below 0.5% (outermost guard-layer bookkeeping) and does not accumulate over steps,
• the profile response is confined to smoothing genuine deposit structure.

Notes for review (draft)

1. RZ benchmark checksums of filtered tests will shift and need resetting once the approach is agreed on.
2. Physics tests with tight tolerances tuned against the old filter should be re-examined: on one RZ deck whose axis deposit structure the two filters smooth differently, an electron-energy adiabat metric moved from 0.6% to 2.6% median.
3. The flux-form sweeps fill one guard layer fewer per pass than the stencil form; the outermost guard layer keeps the raw deposit values and the guard sum is clamped to the well-defined region.
4. Face weights are arithmetic means of the point volume factors; exact annulus areas are a possible refinement.
5. Compensation: warpx.use_filter_compensation is only consumed by the PSATD k-space filter; the real-space BilinearFilter is purely binomial, so nothing else needs changing here. If a real-space compensator is ever added, it folds directly into this design: the (-a, 1+2a, -a) sharpening pass is one more flux-form sweep with coefficient -npass/4, and conservation/constant-preservation are properties of the flux structure independent of the sweep coefficient.

🤖 Generated with Claude Code

https://claude.ai/code/session_01FyFeNNpr5jir3ygSakbZCm

[clarkse-he]

Conservation evidence: flux-form filter vs. development

Setup: hybrid-PIC RZ (the solver that permits radial filter passes), 64×128, m=0,
axis-peaked Gaussian proton column (σ_r ≈ 8 Δr) with a small axial drift,
periodic z, filter applied to the fresh ρ/J deposits every step. Metric: the
code-native volume quadrature Σ w·u (2πr off axis, π Δr f_axis on axis — the
same convention as the inverse-volume-scaling routines) of the raw staggered
rho_fp/jz_fp, for each filtered run against an unfiltered twin. Deposition
conserves the twin's integral exactly, so the ratio isolates the filter.

• Left — 100-step hybrid run, standard 1 pass/direction: development
  creates/destroys 2–4×10⁻³ of the total charge as a persistent systematic
  (bias concentrated near the axis); this branch sits at the measurement floor
  (≤ 2×10⁻¹⁶ early, ≤ 10⁻⁹ late, the late rise being the twin's own slow drift).
• Right — ballistic twins (E = B = 0, so filtered/unfiltered particles stay
  bit-identical and the floor is pure roundoff): development's error grows
  linearly with pass count for both total charge and total axial current,
  reaching 2.4×10⁻² at 8 passes; this branch stays ≤ 4×10⁻¹⁶ for both
  quantities at every pass count.

The npass sweep is also what exposed the guard-budget issue fixed in
e012480: the filter's working arrays now carry 2·npass extra guard layers,
so the subsequent guard-cell sum only ever folds filtered data.