Non-intrusive reduced-order modelling of coupled fluid-material physics at ablating interfaces

Designing thermal protection systems for atmospheric reentry requires simulating the coupled physics of a (possibly ablating) reacting solid and a super/hypersonic flow. The computational bottleneck is often the computational fluid dynamics solver, which, in the presence of severe CFL constraints, is orders of magnitude more expensive than the material response solver. While we can afford to compute the material response using the governing equations, the computational cost of solving the fluid dynamics equations must be reduced by developing reduced-order models that capture the behavior of the fluid in response to the material dynamics.

We develop reduced-order models for the fluid dynamics using a novel, non-intrusive paradigm. Inspired by the form of projection-based reduced-order models, we seek reduced-order tensors as well as bases for the test and trial subspaces by minimizing the error between ground-truth observations and the predictions provided by the reduced-order model. The domain of the optimization problem is a product manifold of several Euclidean spaces (as many as the number of tensors we wish to fit) with a Grassmann manifold and a Stiefel manifold. The optimization can be performed non-intrusively in the sense that the gradient of the cost function with respect to the parameters does not require quering the full-order fluid dynamics solver. The resulting models are demonstrated on the Mach-2 flow over an ablating wedge.