In reduced-order model (ROM) development for reacting flow simulations, data-driven principal component analysis (PCA) for dimensionality reduction and the physics-based computational singular perturbation (CSP) for temporal stiffness reduction have demonstrated their effective roles in accelerated computing without losing fidelity. The present study proposes a new algorithm to combine the benefits of both methods by a double mapping operation from the state-space to time-decoupled and lower-dimensional PCA-CSP latent variables. In this approach, the complex reactive systems are first mapped onto the orthogonal space by the PCA projection, followed by the dynamical time scale decomposition by CSP operated on the PC-score variables, such that the time integration is performed on the active modes using the G-scheme algorithm. The mathematical formulation is described in detail to prove that the combined linear projections preserve the dynamical properties of the original system in terms of the spectral range and gaps of the eigenvalues. To further confirm the validity of the method in a truncated system of PCs, ignition of homogeneous ammonia/air and propane/air mixtures with detailed chemistry was adopted as test problems. Results show that the application of CSP on the truncated PCs preserves nearly the same stiffness properties, and that the reduced number of PC-score transport equations can be integrated using the G-scheme at the active mode time scale that is much larger than the smallest time scale of the original system. Significant additional computational savings are achieved through the eigenvalue decomposition of the much smaller Jacobian matrix of the PC scores. The results suggest a potential for the PCA/G-scheme algorithm to achieve substantial acceleration of high-fidelity reacting flow simulations in large dimensions involving large number of variables with a wide spectrum of time scales.
A combined PCA-CSP solver for dimensionality and stiffness reduction in reacting flow simulations / Malik, M. R.; Malpica Galassi, R.; Valorani, M.; Im, H. G.. - In: PROCEEDINGS OF THE COMBUSTION INSTITUTE. - ISSN 1540-7489. - 40:1-4(2024). [10.1016/j.proci.2024.105532]
A combined PCA-CSP solver for dimensionality and stiffness reduction in reacting flow simulations
Malpica Galassi R.
;Valorani M.;
2024
Abstract
In reduced-order model (ROM) development for reacting flow simulations, data-driven principal component analysis (PCA) for dimensionality reduction and the physics-based computational singular perturbation (CSP) for temporal stiffness reduction have demonstrated their effective roles in accelerated computing without losing fidelity. The present study proposes a new algorithm to combine the benefits of both methods by a double mapping operation from the state-space to time-decoupled and lower-dimensional PCA-CSP latent variables. In this approach, the complex reactive systems are first mapped onto the orthogonal space by the PCA projection, followed by the dynamical time scale decomposition by CSP operated on the PC-score variables, such that the time integration is performed on the active modes using the G-scheme algorithm. The mathematical formulation is described in detail to prove that the combined linear projections preserve the dynamical properties of the original system in terms of the spectral range and gaps of the eigenvalues. To further confirm the validity of the method in a truncated system of PCs, ignition of homogeneous ammonia/air and propane/air mixtures with detailed chemistry was adopted as test problems. Results show that the application of CSP on the truncated PCs preserves nearly the same stiffness properties, and that the reduced number of PC-score transport equations can be integrated using the G-scheme at the active mode time scale that is much larger than the smallest time scale of the original system. Significant additional computational savings are achieved through the eigenvalue decomposition of the much smaller Jacobian matrix of the PC scores. The results suggest a potential for the PCA/G-scheme algorithm to achieve substantial acceleration of high-fidelity reacting flow simulations in large dimensions involving large number of variables with a wide spectrum of time scales.File | Dimensione | Formato | |
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