Aero-thermo-Elastic Trajectory & Hypersonic Estimation Research
A fixed-grid spectral method for coupled moving-boundary problems, with batched uncertainty quantification.
Moving-boundary problems are usually solved on a mesh that moves with the front. That costs twice: interpolation error wherever coupled fields exchange data across a deforming interface, and a remesh per sample, which is what makes Monte Carlo over such problems expensive.
Immobilize the boundary instead. Under a Landau coordinate transformation the front becomes stationary, the spatial operator is assembled once, and the same operator then serves every field, every timestep, and every UQ sample. The third of those is the interesting one: because the operator no longer depends on the sample, an M-sample ensemble collapses to a single batched tensor solve.
Three contributions, stated narrowly:
- Boundary immobilization extended from the scalar heat equation to coupled moving-boundary multiphysics, as a single autonomous ODE system.
- A well-conditioned ultraspherical formulation with an explicit conditioning and stiffness bound, and the IMEX splitting it implies.
- The observation that immobilization is precisely what collapses moving-boundary UQ to one batched operator — with a measured speedup curve.
Immobilization is Landau (1950) and the ultraspherical basis is Olver–Townsend; what is new here is the synthesis and its consequences.
The manuscript is in manuscript/ and is the primary
deliverable of this repository.
cd manuscript && make # or ./build.sh| Module | Contents |
|---|---|
spectral/ |
Chebyshev–Gauss–Lobatto operators by direct recurrence with the negative-sum trick; Clenshaw–Curtis quadrature; barycentric interpolation |
ultraspherical/ |
Olver–Townsend banded operators and assembly |
thermal/ |
Landau immobilization frame; semi-discrete charring/Stefan solver on the fixed grid |
structures/ |
Variable-rigidity Euler–Bernoulli operator; free-free BCs by null-space projection; modal reduction; integrators |
plates/ |
Mindlin plates, laminate stiffness |
coupling/ |
Quadrature-normalized kernel force transfer |
batch/ |
NumPy/CuPy backend abstraction; batched common-outer-grid integrator; sampling; occupancy model |
atmosphere/ |
US Standard 1976, MSIS thermosphere, ERA5 reanalysis winds |
dynamics/ |
Quaternion attitude kinematics, deformed-surface incidence |
verification/ |
Executable verification tasks |
pip install -e .[dev]
pip install -e .[atmosphere] # optional: MSIS thermosphere
pip install -e .[cuda] # optional: GPU batch backendpytest tests -q # 331 tests
python -m aether.verification # verification tasks -> results/
python tools/check_boundary.py # scope check, see belowThis package is deliberately limited to numerical-methods and standard-published-model content. Applied flight-systems capability — guidance, trajectory optimization, sensing, tracking, and engagement modelling — is developed separately and is not distributed here.
That boundary is enforced mechanically rather than by convention:
tools/check_boundary.py fails the build on any import reaching outside
the public kernel. Run it before publishing, and after moving any module
in either direction.
MIT. See LICENSE.