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dai M M dφj M d2φj dt + ajφj aj dx,φi−μ aj dx2 ,φi =0, i=1,...,M (6.21) j=1 j=1 j=1 Thus, the reduced-order model comprises only M ODEs. Equation (6.19) was first discretized in space using a simple finite difference scheme with 50 spatial nodes (Nx = 50). The resulting set of ODEs was then integrated in MATLAB using Chapter 6. Reduced-order Modeling for Optimization 109 6.3 Reduced-order Modeling Figure 6.1: Comparison of original profile and ROM profiles for Burgers equation for varying subspace dimension Here we use an L2 inner product since the snaphots are obtained after spatial discretization of the PDE which lead to POD basis vectors (not basis functions). After simplification and applying orthonormality of the basis functions, we obtain our reduced-order model which is given asPDF Image | Design and Operation of Pressure Swing Adsorption Processes
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