Metadata-Version: 2.4
Name: ideal-gases
Version: 0.1.4
Summary: Compute classical and quantum Euler solutions
Keywords: riemann,euler,quantum,polylogarithm,cfd
Author-Email: "Manuel A. Diaz" <manuel.ade@gmail.com>
License-Expression: MIT
License-File: LICENSE
Classifier: Development Status :: 4 - Beta
Classifier: Intended Audience :: Science/Research
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.11
Classifier: Programming Language :: Python :: 3.12
Classifier: Programming Language :: Python :: 3.13
Classifier: Programming Language :: Python :: 3.14
Classifier: Topic :: Scientific/Engineering :: Physics
Project-URL: Homepage, https://github.com/wme7/ideal-gases
Project-URL: Repository, https://github.com/wme7/ideal-gases
Project-URL: Issues, https://github.com/wme7/ideal-gases/issues
Requires-Python: >=3.11
Requires-Dist: numpy>=2.0
Provides-Extra: plot
Requires-Dist: matplotlib>=3.9; extra == "plot"
Provides-Extra: progress
Requires-Dist: tqdm>=4.66; extra == "progress"
Description-Content-Type: text/markdown

# Classical and Quantum Ideal Gases

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Exact Riemann solvers for classical and quantum Euler gases, 1-D Navier–Stokes–Fourier (NSF) solvers, and a fast polylogarithm kernel used to resolve the quantum equation of state.

This repository ports the MATLAB implementation found in [this thesis](https://doi.org/10.6342/NTU.2015.00509) to Python 3.11. The polylog function has been ported from the MATLAB implementation to C++ and the Toro exact Riemann solver has been extended to support Fermi–Dirac (FD), Bose–Einstein (BE), and Maxwell–Boltzmann (MB) statistics.

## Requirements

- Python 3.11+
- [pip](https://pip.pypa.io/) (or [uv](https://docs.astral.sh/uv/))

Building from source additionally requires a C++17 compiler. See [DEVELOPER_GUIDE.md](DEVELOPER_GUIDE.md).

## Installation

```bash
pip install ideal-gases
```

For plotting (`euler plot`, interactive explorers):

```bash
pip install ideal-gases[plot]
```

After install, the `euler` command-line tool is available.

## Interactive mode

Launch matplotlib widget explorers to build custom Riemann problems with sliders, statistic toggles (quantum), and Save/Reset controls. Y-axis limits autoscale automatically on each update.

```bash
euler interactive classical
euler interactive quantum
```

Seed the initial state from CLI flags or a JSON config (same fields as `euler solve`):

```bash
euler interactive classical --gamma 1.4 --t-end 0.5 --nx 101
euler interactive quantum --rho-l 2 --t-l 1.5 --n 3 --h 0.5
euler interactive classical --config case.json
```

Optional domain flags (`--x-min`, `--x-max`, `--x0`, `--nx`) default to an interactive Sod-tube layout (`x` in `[-10, 10]`, discontinuity at `x0=0`, `nx=1024`). Use `-f path.png` to set the **Save** button target; nothing is written until you click Save.

### Example usage

```bash
euler interactive quantum
```
Outputs a Sod shock tube problem resolved with a quantum Euler solver for all statistics. We deactivate the solutions of MB and BE to focus on the FD solution. Using the slider, we can vary the left and right states and the thermal scale parameter `h` and the number of degrees of freedom `n` of the gas.

In Fig. 5 of [Hu and Jing (2010)](https://www.researchgate.net/profile/Shi-Jin-5/publication/228568274_On_kinetic_flux_vector_splitting_schemes_for_quantum_Euler_equations/links/02e7e525327fccc0cf000000/On-kinetic-flux-vector-splitting-schemes-for-quantum-Euler-equations.pdf), a fictitious 2-d fermi gas degenerate regime is used to prove the accuracy of Kinetic Flux Vector Splitting schemes for quantum Euler equations. Using the interactive mode, we set `n` : 2 and set the left and right states ($\rho,u,\theta$). Using the `h` slider, we found that the degenerate gas is resolved approximately for `h` $\approx$ 3.71.
As show in the following figure:

![Sod shock tube](https://raw.githubusercontent.com/wme7/ideal-gases/master/figures/fermi_2d_gas_yang_hsieh_shi.png)


## Command-line mode

Compute exact solution profiles, save plots to PNG, and write CSV/JSON files with the solution fields.

### Classical Sod shock tube

```bash
euler solve classical \
  --rho-l 1 --u-l 0 --p-l 1 \
  --rho-r 0.125 --u-r 0 --p-r 0.1 \
  --t-end 0.25 --gamma 1.4 \
  --nx 101 -o sod.csv
```

### Quantum Euler

```bash
euler solve quantum \
  --rho-l 1 --u-l 0 --t-l 1 \
  --rho-r 0.125 --u-r 0 --t-r 0.25 \
  --t-end 0.20 --n 2 --h 0.1 --statistic FD \
  -o euler_fd.csv
```

Write separate files for FD, MB, and BE with `--all-statistics` (e.g. `euler_case7_FD.csv`, `euler_case7_MB.csv`, `euler_case7_BE.csv`):

```bash
euler solve quantum ... --all-statistics -o euler_case7
```

### Equilibrium inversions

Compute the fugacity from density and temperature:

```bash
euler fugacity --rho 1.0 --theta 1.0 --n 3 --h 1.0 --statistic FD
```

Recover fugacity, temperature and pressure from density and internal energy:

```bash
euler moments --rho 1.0 --e 1.5 --n 3 --h 1.0 --statistic FD
```

Use `-o result.json` to write JSON output instead of printing to stdout.

### Built-in benchmarks

```bash
euler toro 1 -o toro_test1.csv
euler list --toro

euler quantum-example 7 --all-statistics -o euler_eg7
euler list --quantum
```

### JSON config files

Define a problem in JSON and run it with `euler run` or pass `--config` to `euler solve`:

```bash
euler run --config case.json
euler solve classical --config case.json -o override.csv
```

Example `case.json`:

```json
{
  "mode": "quantum",
  "left": {"rho": 1.0, "u": 0.0, "theta": 1.0},
  "right": {"rho": 0.125, "u": 0.0, "theta": 0.25},
  "t_end": 0.20,
  "n": 2.0,
  "h": 0.1,
  "statistic": "FD",
  "all_statistics": true,
  "format": "json",
  "output": "euler_case7",
  "domain": {"x_min": 0.0, "x_max": 1.0, "x0": 0.5, "nx": 101}
}
```

Use `--format json` (or a `.json` output path) for JSON instead of CSV. CLI flags override values from the config file.

### Visualization

Save a classical Sod shock tube figure:

```bash
euler plot classical \
  --rho-l 1 --u-l 0 --p-l 1 \
  --rho-r 0.125 --u-r 0 --p-r 0.1 \
  --t-end 0.2 --gamma 1.4 --nx 101 \
  -f sod.png
```

Plot a single quantum statistic or compare FD/MB/BE:

```bash
euler plot quantum \
  --rho-l 1 --u-l 0 --t-l 1 \
  --rho-r 0.125 --u-r 0 --t-r 0.25 \
  --t-end 0.20 --n 2 --h 0.1 --statistic FD \
  -f qfd.png

euler plot quantum-example 7 --all-statistics -f eg7
```

With `--all-statistics`, `-f eg7` writes `eg7_panels.png` (3×6 grid) and `eg7_comparison.png` (overlay). Use `--layout panels|comparison|both` to select one or both (default: `both`). Add `--show` for an interactive window, or `-o` to export CSV/JSON in the same run.

### Example usage

In [Filbet, Hu and Jing (2010)](https://www.cambridge.org/core/journals/esaim-mathematical-modelling-and-numerical-analysis/article/abs/numerical-scheme-for-the-quantum-boltzmann-equation-withstiff-collision-terms/BFB7B0297D8BC201F9A2C9008F4894BC), the authors use a Sod shock tube initial condition with a fictitious 2-d fermi and bose gas to prove the accuracy of their numerical scheme in classical and quantum hydronamic regimes. These are examples 7 and 8, respectively, in the CLI plot tool.

```bash
euler plot quantum-example 7 --all-statistics -f sod_2d_gas_classical --layout comparison --show
```
yields the following plot:
![Sod shock tube](https://raw.githubusercontent.com/wme7/ideal-gases/master/figures/sod_2d_gas_classical_comparison.png)

```bash
euler plot quantum-example 8 --all-statistics -f sod_2d_gas_quantum --layout comparison --show
```
yields the following plot:
![Sod shock tube](https://raw.githubusercontent.com/wme7/ideal-gases/master/figures/sod_2d_gas_quantum_comparison.png)

## Python module

Import `ideal_gases` to compute classical and quantum Euler and NSF solutions in your own scripts.

### Classical Euler

```python
import numpy as np
from ideal_gases import classical_euler

x = np.linspace(0.0, 1.0, 101)
result = classical_euler(
    rho_l=1.0,
    u_l=0.0,
    p_l=1.0,
    rho_r=0.125,
    u_r=0.0,
    p_r=0.1,
    t_end=0.2,
    gamma=1.4,
    x=x,
    x0=0.5,
)
```

### Quantum Euler (FD / BE / MB)

Left and right states are given in terms of density `rho`, velocity `u`, and temperature `theta` (written `t` in the API). The solver converts these to effective pressures via the quantum EOS, then applies the Toro exact Riemann solver.

```python
import numpy as np
from ideal_gases import quantum_euler

x = np.linspace(0.0, 1.0, 101)
result = quantum_euler(
    rho_l=1.0,
    u_l=0.0,
    t_l=1.0,
    rho_r=0.125,
    u_r=0.0,
    t_r=0.25,
    t_end=0.20,
    n=2.0,          # degrees of freedom; gamma = (n+2)/n
    h=0.1,          # thermal scale parameter
    statistic="FD", # "FD", "BE", or "MB"
    x=x,
    x0=0.5,
)
```

This returns a `RiemannResult` object that contains the solution fields: `x`, `rho`, `ux`, `p`, `e`, `z` (fugacity), `t` (temperature), `mach`, `entropy`.

In the classical limit, MB statistics with `h → 0` recover the ideal-gas behaviour (pressures `p = rho * theta`).

### Classical NSF

1-D Navier–Stokes–Fourier for a monatomic ideal gas. Same Sod left/right states as the classical Euler example; `dim` in `{1, 2, 3}` sets `γ = (dim+2)/dim` (unlike Euler's free `gamma`). `kn` is the Knudsen number used by the Chapman–Enskog closure `μ = kn ρ T`.

```python
import numpy as np
from ideal_gases import classical_nsf

x = np.linspace(0.0, 1.0, 101)
result = classical_nsf(
    rho_l=1.0,
    u_l=0.0,
    p_l=1.0,
    rho_r=0.125,
    u_r=0.0,
    p_r=0.1,
    t_end=0.2,
    dim=3,
    kn=0.01,
    x=x,
    x0=0.5,
)
```

This returns a `ClassicalNSFResult` object that contains the cell-centered fields: `rho`, `u`, `t` (temperature), `p`, `q` (heat flux).

### Quantum NSF (FD / BE / MB)

1-D Navier–Stokes–Fourier with the quantum EOS. Same left/right states as the quantum Euler example; `dim` replaces Euler's `n`, and `kn` sets the Chapman–Enskog viscosity `μ = kn p(z)`.

```python
import numpy as np
from ideal_gases import quantum_nsf

x = np.linspace(0.0, 1.0, 101)
result = quantum_nsf(
    rho_l=1.0,
    u_l=0.0,
    t_l=1.0,
    rho_r=0.125,
    u_r=0.0,
    t_r=0.25,
    t_end=0.20,
    dim=2,
    h=0.1,
    kn=0.01,
    statistic="FD", # "FD", "BE", or "MB"
    x=x,
    x0=0.5,
)
```

This returns a `QuantumNSFResult` object (`NSFResult` is an alias) that contains: `rho`, `u`, `t`, `p`, `z` (fugacity), `q` (heat flux).

### Equilibrium inversions

Given density and temperature, recover the fugacity:

```python
from ideal_gases import find_fugacity

z = find_fugacity(rho=1.0, T=1.0, dim=3, h=1.0, eta=-1)
```

Given density and internal energy, recover fugacity, temperature and pressure:

```python
from ideal_gases import find_moments

z, T, p = find_moments(rho=1.0, e=1.5, dim=3, h=1.0, eta=-1)
```

The `eta` parameter selects the statistic: `-1` Fermi, `0` classical (Maxwell-Boltzmann), `+1` Bose.

### Polylogarithm module

Quantum solvers (`G`, `find_moments`, `quantum_euler`) and `polylog(n, z)` use the unified C++ kernel: Fukushima minimax Fermi–Dirac / Bose–Einstein integrals for supported half-integer orders on `z < 0` and `0 < z < 1`, with [Bhagat](https://doi.org/10.1016/S0010-4655(03)00294-7) / integer analytic branches as fallback.

We can use the polylogarithm module on our scripts as follows:

```python
import numpy as np
from ideal_gases import polylog

polylog(2, 0.5)                         # scalar
polylog(1.5, np.linspace(0.2, 0.9, 50)) # array
```

We can plot the polylogarithm function to verify the accuracy of the implementation for integer and half-integer orders as follows:

```bash
uv run scripts/plot_polylogarithms.py
```
yields the following plot:
![Polylogarithm](https://raw.githubusercontent.com/wme7/ideal-gases/master/figures/polylogarithms.png)

### Public API

```python
from ideal_gases import (
    G,
    ClassicalNSFResult,
    QuantumNSFResult,
    RiemannResult,
    adiabatic_index,
    classical_euler,
    classical_nsf,
    equilibrium_moments,
    find_fugacity,
    find_moments,
    polylog,
    quantum_euler,
    quantum_nsf,
)
```

| Symbol | Role |
|--------|------|
| `polylog(n, z)` | Fast C++ polylogarithm (Fukushima + Bhagat/integer fallback) |
| `adiabatic_index(n)` | Returns γ = (n + 2) / n |
| `classical_euler(...)` | Classical ideal-gas exact Euler Riemann solver |
| `quantum_euler(...)` | Quantum EOS + Toro exact Euler Riemann solver |
| `classical_nsf(...)` | 1-D classical Navier–Stokes–Fourier solver |
| `quantum_nsf(...)` | 1-D quantum Navier–Stokes–Fourier solver |
| `RiemannResult` | Euler solution profiles on the spatial grid |
| `ClassicalNSFResult` | Classical NSF fields (`rho`, `u`, `t`, `p`, `q`) |
| `QuantumNSFResult` | Quantum NSF fields (`rho`, `u`, `t`, `p`, `z`, `q`) |
| `G(n, z, eta)` | Bose / Fermi / classical partition function |
| `equilibrium_moments(z, T, ...)` | Forward map (z, T) → (ρ, e) |
| `find_fugacity(rho, T, ...)` | Invert (ρ, T) → z |
| `find_moments(rho, e, ...)` | Invert (ρ, e) → (z, T, p) |

## License

MIT License. See [LICENSE](LICENSE) for the full text.

Copyright (c) 2026 Manuel A. Diaz

For building from source, tests, linting, CI, and releases, see [DEVELOPER_GUIDE.md](DEVELOPER_GUIDE.md).
