LinearEuler 2D/3D: variable background density via static nodal rho0

[fluidnumericsJoe]

Summary

Adds support for a spatially-varying background density rho0 to the LinearEuler 2D and 3D models, so heterogeneous media with both density and sound-speed contrast are supported. This mirrors the heterogeneous sound-speed pattern merged in #138: rho0 is promoted from a scalar model attribute to a static per-node solution variable (zero flux, zero source, excluded from time integration via nstepped).

• 2D: nvar 5→6 (rho0 = variable 6), nstepped stays 4.
• 3D: nvar 6→7 (rho0 = variable 7); also sets nstepped=5 (previously unset — the 3D model relied solely on zero flux/source to hold c static).

The interior flux, entropy_func, and the impedance-matched Riemann flux now read the per-node rho0. The Riemann solver uses the per-side impedance Z = rho0*c, so material interfaces (density and/or sound-speed jumps) get the physically correct reflection/transmission; the reconstructed density/momentum/pressure fluxes use the face-averaged rho0 and c^2 (the same pragmatic treatment already used for c^2). The scalar rho0 attribute is retained as the reference value used to fill the field in the built-in initial conditions.

Entropy stability

For piecewise-constant material regions aligned with element boundaries (the target regime — e.g. tissue/bone imaging), element interiors have ∇rho0 = ∇c = 0 so the flux-divergence form is exactly entropy-conservative, and the impedance-matched Riemann flux carries the entropy-stable interface dissipation. (A fully entropy-conservative split-form treatment for smoothly-varying media on ECDGModel is tracked separately as SELF-24.)

Changes

• GPU: fluxmethod/boundaryflux kernels read per-node rho0 and drop the scalar rho0 argument; BC kernels copy rho0 through to the exterior state (signatures now mirror the c handling in LinearEuler3D: heterogeneous sound speed + impedance-matched Riemann flux #138).
• New CPU radiation BC for the 2D model (previously only the GPU backend registered one): zeros the acoustic perturbation and copies c and rho0, mirroring the 3D model.
• PML: added an entropy_func override so the PML variant keeps using its scalar rho0 (its variable 6 is the auxiliary phi_rho, not rho0).
• Fixed the 2D entropy_func s(3)*(3) typo (already fixed for 3D in LinearEuler3D: heterogeneous sound speed + impedance-matched Riemann flux #138).
• boneandmarrow example: stamps a per-material rho0 (muscle/bone/marrow) alongside c, exercising a genuinely heterogeneous impedance field.
• planewave examples: set the new rho0 variable in the IC and the prescribed boundary state.
• Updated the 2D/3D model docs.

Testing

CPU (gfortran, GPU OFF) build is clean; all 7 LinearEuler ctests pass:

lineareuler2d_pml_absorption ...................... Passed
linear_euler2d_spherical_soundwave_closeddomain ... Passed
linear_euler2d_planewave_reflection ............... Passed
linear_euler2d_planewave_propagation .............. Passed
linear_euler2d_pml_planewave ...................... Passed
linear_euler2d_boneandmarrow ...................... Passed
linear_euler3d_spherical_soundwave_radiation ...... Passed

linear_euler2d_boneandmarrow (variable density + variable sound speed) entropy is finite and monotonically decreasing (final/initial ≈ 0.998), with the rho0 field correctly heterogeneous (min=0.93, max=1.8).

GPU kernel changes were not exercised by the CPU build — relying on Buildkite GPU CI to validate.

🤖 Generated with Claude Code

[makeplane]

Linked to Plane Work Item(s)

References

• (SELF-24) Entropy-conservative LinearEuler on ECDGModel for smoothly-varying media

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