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A projection-based formulation is presented for non-linear model reduction ofproblems with extreme scale disparity. The approach allows for the selection ofan arbitrary, but complete, set of solution variables while preserving thestructure of the governing equations. Least-squares-based minimization isleveraged to guarantee symmetrization and discrete consistency with thefull-order model (FOM). Two levels of scaling are used to achieve theconditioning required to effectively handle problems with extremely disparatephysical phenomena, characterized by extreme stiffness in the system ofequations. The formulation -- referred to as model-form preservingleast-squares with variable transformation (MP-LSVT) -- provides globalstabilization for both implicit and explicit time integration schemes. Toachieve computational efficiency, a pivoted QR decomposition is used withoversampling, and adapted to the MP-LSVT method. The framework is demonstratedin representative two- and three-dimensional reacting flow problems, and theMP-LSVT is shown to exhibit improved stability and accuracy over standardprojection-based ROM techniques. Physical realizability and local stability arepromoted by enforcing limiters in both temperature and species mass fractions.These limiters are demonstrated to be important in eliminating regions ofspurious burning, thus enabling the ROMs to provide accurate representations ofthe heat release rate and flame propagation speed. In the 3D application, it isshown that more than two orders of magnitude acceleration in computationalefficiency can be achieved, while also providing reasonable future-statepredictions. A key contribution of this work is the development anddemonstration of a comprehensive ROM formulation that targets highlychallenging multi-scale transport-dominated problems.

Model Reduction for Multi-Scale Transport Problems using Model-form Preserving Least-Squares Projections with Variable Transformation