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Boundaries

Where PyIMR stops, and where it deliberately parts company with IMRv2.

Conventions

  • PhysicalParameters defaults reproduce the pinned reference trajectories. The default polytropic exponent is 1.4; IMRv2 itself ships with 1.47.
  • SimulationResult.stress_state contains nondimensional internal variables. Public dimensional outputs carry units in their names or documentation.
  • Collapse shooting requires a material with memory, and cannot be combined with an explicit initial stress state or a nonzero observed wall velocity. IMRv2 does permit collapse for memoryless materials, which PyIMR deliberately does not.

Deliberate divergences

  • gilmore with liquid_eos="mie-gruneisen" (upstream radial = 6) is supported here, and is the one configuration IMRv2 cannot run at all -- upstream returns complex radii without raising. The cause is a wrong root of the Mie-Gruneisen density quadratic; see upstream.md.
  • Both Mie-Gruneisen operators (upstream radial = 5 and 6) deliberately diverge from IMRv2. Upstream's Mie-Gruneisen branch is physically wrong; the corrections are validated against the independent Tait branches and the weakly-compressible limit rather than against upstream. tests/ref_radial5.csv is retained as a record of upstream behaviour, not as a target.

Reference implementation

PyIMR reproduces IMRv2 except where upstream is wrong. One divergence is numerical rather than a defect fix: the Zener acceleration coefficient, which makes three Zener reference trajectories regression pins rather than cross-checks (#174).

Eight defects were found at dea31cd, each reproduced with MATLAB R2025a via tools/gen_imrv2_cases.m, and each correction validated against something other than upstream -- a closed form, an independent equation of state, or a reduction limit. The wrong Mie-Gruneisen root, the non-functional non-Newtonian viscosity suite, the stubbed collapse initialization and the rest are in upstream.md.

Those defects are why several PyIMR models are validated by reduction limit rather than against a pinned upstream trajectory: for those models, no working upstream implementation exists to pin against.

The sonic line

The first-order-in-Mach dynamics divide by

$$ \left[1-(\lambda+1)\frac{\dot R}{c}\right]R + \frac{\text{(acceleration coefficient)}}{c}, $$

which vanishes as an outward-moving wall reaches $c/(\lambda+1)$ -- the sound speed for keller-miksis and keller-enthalpy, half of it for herring. Going inward the same factor grows, so a supersonic collapse is nowhere near the singularity while a supersonic rebound is the singularity.

A stiffening law can drive a bubble there. On the #245 band a Yeoh RelaxingMaterial collapses, arrests, and rebounds onto that denominator: $\dot R$ climbs to $c$ to six digits while the radius sits still and the step size falls to machine epsilon. The solve then reports "maximum number of solver steps", which reads as a budget problem and is not one -- the trajectory approaches the singularity from below and never arrives, so no budget, tolerance, solver or quadrature setting reaches the far side.

max_wall_mach refuses that case by name instead, as a solver event. It is off by default, one-sided, and deliberately not the same guard as min_radius_ratio: the two order runs differently. On that band a relaxation time of $10^{-3}$ integrates cleanly through $R/R_0 = 0.010186$, while $6.81\times10^{-6}$ dies stalled at $0.010447$ -- above the depth the healthy one survives, so every radius floor is on the wrong side of one of them. Peak wall Mach separates the pair cleanly, $0.312$ against $0.99999$.

Values above one are accepted rather than rejected as typos: rayleigh-plesset is incompressible, has no such denominator, and genuinely exceeds Mach one.

Tangent equations

Forward sensitivities integrate

$$ \frac{ds_k}{dt}=J_y s_k+\frac{\partial f}{\partial c_k}. $$

All requested parameter directions share one augmented integration. Prepared parameter scaling keeps error control dimensionless; public derivatives are converted back to dimensional parameter units.

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