Direct numerical simulation with time dependent subspaces for reduced-order modeling (ROM) of turbulent compressible reacting flows

Development of accurate predictive models in compressible reacting flows for practical fuels requires solving a large number of species transport equations. This can become computationally intractable for complex alternative fuels including sustainable aviation fuel surrogates or even blends of methane with hydrogen. At the same time, such flow-flame interactions are often characterized by the presence of strongly transient events associated with finite-time instabilities including auto-ignition, extinction, re-ignition etc. whose detection through infinite-time methods, e.g., long term averages or information about the statistical steady-state, is not possible. In this work, the performance of dynamically bi-orthogonal (DBO) decomposition [D. Ramezanian et al., Comput. Methods Appl. Mech. Engrg. 382 (2021) 113882] is evaluated for the reduced-order modeling (ROM) of compressible reacting flows in the context of DNS performed on heterogeneous supercomputers. DBO is an on-the-fly low-rank approximation technique in which the instantaneous composition matrix of the reactive flow field is decomposed into a set of orthonormal spatial modes, a set of orthonormal vectors in the composition space, and a factorization of the low-rank correlation matrix. This approach bypasses the need to solve the full-dimensional set of species transport equations to generate high-fidelity data as is commonly performed in data-driven dimension reduction techniques such as the principal component analysis (PCA). A demonstration case of DBO-based ROM of reacting transport equations exhibiting strongly transient combustion phenomena including flame propagation and extinction is presented using a methane-hydrogen mechanism. A-posteriori comparisons against the data generated via full-rank direct numerical simulation (DNS) as well as the instantaneous PCA reduction of the DNS data is carried out to assess the effectiveness and accuracy of the DBO based ROM of turbulent compressible reacting flows.