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Linear time varying (LTV) systems are commonly applied in commercial PDE solvers. Large scale nonlinear PDE-based models are usually discretised by computational techniques that lead to LTV formulation. Proper orthogonal decomposition has been largely employed to reduce numerical PDE-based models, however computational saving is often far below the expected rate in spite of the dramatic reduction of the original order. We address a practical solution to this problem by only conducting Galerkin projection onto pre-selected state variables and estimate the rest by the known POD basis vectors. The technique saves considerable computational effort needed to obtain a reduced order model and enables fast prediction of the future states, which is essential for control design.