Bubble sound speed: alpha -> 1 should assert, not silently produce Inf

[sbryngelson]

Summary

The bubble-mixture branch of s_compute_speed_of_sound is an O(alpha) expansion whose alpha is the
dilute bubbly void fraction the user supplies. When alpha approaches one the expansion has left its
regime, and the code responds by silently producing +Inf rather than saying so.

A floor on (1 - alpha) would be the wrong fix - it would let a bad index or an out-of-regime case run
on quietly. What is wanted is a diagnostic that names the actual condition.

The branch is just the liquid sound speed with a void correction

rho under bubbles_euler is the liquid partial density, (1 - alpha) rho_l, and gamma/pi_inf are
the carrier liquid's own coefficients. So

c^2 = K_l / (rho (1 - alpha))  =  K_l / (rho_l (1 - alpha)^2)  =  c_l^2 / (1 - alpha)^2

that is,

c = c_l / (1 - alpha), with c_l = sqrt(K_l/rho_l) the pure carrier-liquid sound speed.

m_qbmm.fpp:775 forms that same c_l directly - f_bulk_modulus(pres, gammas(1), pi_infs(1))*(1 - alf)/rho

• for Keller-Miksis, and is independent of alpha as a pure-liquid property should be. Verified numerically:

alpha	c_qbmm^2 (= c_l^2)	c from this branch	c_l/(1 - alpha)
0.00	21981.075	148.2602	148.2602
0.04	21981.075	154.4377	154.4377
0.20	21981.075	185.3252	185.3252
0.50	21981.075	296.5203	296.5203

Written this way three things become readable that the current form hides: it is manifestly the O(alpha)
expansion c ~ c_l (1 + alpha); it diverges as alpha -> 1, so a near-one value cannot be a physical
mixture speed; and it is the same quantity m_qbmm computes, differing only by the void correction, so
the two should not be mistaken for competing formulas. (The speed rising with void fraction is correct for
an O(alpha) carrier-phase correction and is why alt_soundspeed exists separately as Wood's law.)

Scope of validity

The expansion is only good in the dilute limit. Outside it neither the Euler-Euler (bubbles_euler) nor
the Euler-Lagrange bubble model is recommended, so a large alpha reaching this line indicates a case
outside the models' intended regime, a wrong index, or both.

What to do

alpha == 1 yields +Inf, which is not < 0, so it passes the mixture_err check and propagates through
sqrt into the wave speeds; alpha > 1 gives a negative c caught only when mixture_err is on (off by
default in the test base config). Either way the failure surfaces far from its cause.

An assertion or diagnostic naming the dilute-limit violation would report the real problem at the point it
occurs. A clamp would not.

Pre-existing on master (src/common/m_variables_conversion.fpp); not introduced by #1762,
which preserves the semantics exactly while centralizing the expression.

Correction to the original report

First filed claiming this division was the mechanism behind NaNs seen on Frontier CCE OpenACC in #1794.
That was wrong. There alpha is nowhere near one: the Lagrange suites run bubbles_lagrange with
bubbles_euler = F and never enter this branch, and the QBMM case has alpha = 4e-2, so the correction is
1/0.96 - which accounts for the measured 1.7% answer shift and nothing more. That NaN mechanism remains
open in #1794.

[sbryngelson]

Ruling (maintainer)

The 1/(1 - alpha) must only ever be fed the subgrid void fraction, which is small by construction.
The fix is structural plus a case-level warning, not a runtime clamp:

1. Structural. Make the code express that this alpha is the subgrid void fraction of the bubble
   phase, so the dilute assumption is visible at the point of use rather than implied. Writing the branch
   as its identity c = c_l/(1 - alpha) (see above) does this: it shows the quantity is the carrier-liquid
   sound speed with a void correction, and that the correction diverges outside the dilute limit.
2. Case-level warning. A bubbles_euler (or Euler-Lagrange) case set up with a void fraction that is
   not small should be served a warning from the Python toolchain at case load - self.warn(...) in
   check_bubbles_euler (toolchain/mfc/case_validator.py), which already has a non-fatal warning
   channel used in five other places. Non-fatal: the model is not recommended outside the dilute limit
   rather than forbidden there.

Explicitly not wanted: a floor on (1 - alpha), which would let a bad index or an out-of-regime case
run on silently, and a device-side assertion, which is impossible anyway - s_compute_speed_of_sound is a
GPU_ROUTINE(parallelism='[seq]'), and both @:ASSERT and @:PROHIBIT expand to s_mpi_abort, which
cannot be called from device code. Neither macro is debug-gated, so there is no zero-cost in-kernel option.

[sbryngelson]

Implemented in #1762 as 3bf05670, per the ruling above.

• Structural: the bubble branch of s_compute_speed_of_sound now binds the void fraction to a named
  alf and states the identity at the point of use - rho is the carrier-liquid partial density, so the
  preceding line is already c_l^2/(1 - alf) and one more division gives c = c_l/(1 - alf), the same
  c_l that m_qbmm:775 forms for Keller-Miksis. The comment says alf is the subgrid void fraction,
  small by construction, and that a value near one means a wrong index or a case outside the expansion's
  regime - not a number to clamp. No arithmetic changed.
• Warning: check_bubbles_euler now emits a non-fatal self.warn when a patch's void-slot alpha
  exceeds DILUTE_VOID_FRACTION_MAX = 0.1. Non-fatal because the model is not recommended outside the
  dilute limit rather than forbidden there.

Verified at 92091a23: 119/119 on Frontier CCE OpenACC and 119/119 on MI210 amdflang OpenMP offload,
across every case carrying an acoustic source or bubbles.

Note the threshold of 0.1 is a judgement call, not a value derived from the model's literature - worth
revisiting if the ensemble-averaged closure has a characterised limit.