Add 1D Beer-Lambert photochemistry solver with Cantera integration

[Copilot]

Implements a one-dimensional photochemistry solver using Beer-Lambert law for actinic flux attenuation, leveraging Cantera's chemical kinetics framework.

Implementation

New directory: examples/BeerLambert1D/ (308 LOC solver + config + docs)

Core algorithm:

// Beer-Lambert attenuation: I(z) = I₀ * exp(-τ)
void computeActinicFlux() {
    for (int k = 0; k < nwavelengths_; k++) {
        double tau = 0.0;
        for (int j = nlevels_ - 1; j >= 0; j--) {
            actinic_flux_(j, k) = toa_flux_(k) * exp(-tau);
            tau += sigma(j, k) * num_density(j) * dz(j);
        }
    }
}

Features:

• Vertical atmospheric grid with exponential pressure profile
• Wavelength-dependent optical depth integration
• Cantera ThermoPhase/Kinetics/Solution integration
• Solar radiation input via existing C3M infrastructure
• Test case: O₂ photolysis network (20 levels, 0-100 km)

Build:

• Standalone CMake config (no modifications to existing build system)
• Optional integration via TASK=BeerLambert
• YAML configuration: beer_lambert_1d.yaml

Follows existing C3M patterns from src/actinic_flux.cpp and tests/1DPP.cpp.

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Original prompt

---

This section details on the original issue you should resolve

<issue_title>Fixing instability in matrix solver</issue_title>
<issue_description>Make a one-dimensional solver for photochemistry using beer-lambert law and leverage the cantera structures to make a cpp file and also one yaml file to test it. Do not modify existing files please</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes Fixing instability in matrix solver #9

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[GalacticBobster]

Extend it by writing an example to solve one dimensional photochemical equilibrium with parameterized eddy and binary diffusion and boundary conditions.