The time-accurate calculations of thermoacoustic instabilities and nonlinear flame dynamics are challenging because of
Aleatoric uncertainties. Under realistic conditions, a thermoacoustic system is subject to stochastic noise, which cannot be exactly replicated in a simulation. In the worst case, the stochastic noise may even trigger combustion instabilities before the limit of linear stability is reached.
Epistemic uncertainties. Combustion instabilities involve hydrodynamic, chemical and acoustic effects among others. A simulation usually relies on some form of compromise, e.g. simplified governing equations, a (relatively) low spatial resolution or a reduced chemical mechanism. The result is a model which may lack relevant degrees of freedom or have inaccurate parameters.
Extreme sensitivity. The long-term behavior of a thermoacoustic system, both qualitative and quantitative, may be highly sensitive to uncertain parameters such as boundary conditions and the operating regime.
We propose to address these challenges by augmenting lower-order models with data from experiments and high-fidelity simulations using methods based on the theory of stochastic processes (with a Bayesian approach) and statistical optimization (with an adjoint-based approach), namely data assimilation and parameter estimation. Data assimilation gives an optimal estimate of the true state of a system given high-fidelity simulation results and experimental measurements. Parameter estimation uses the data to find a maximum-likelihood set of parameters for the model.
