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b M y(x, t) = yb + y + i=1 To incorporate Neumann boundary conditions (homogeneous and non-homogeneous) in this work, we construct a ROM only for the interior spatial domain and boundaries are excluded. In other words, ROMs do not directly determine the solution at the boundaries. We approximate the derivative at boundaries with any finite difference scheme. Based on this approximation together with the boundary condition and the interior solution obtained after integrating ROM, solution at the boundary nodes is determined. 6.3.3 Example - Burgers Equation We illustrate the methodology of constructing a reduced-order model with the help of an example of Burgers equation. Burgers equation represents a wave moving in time with a constant velocity. The wave doesn’t retain its shape and diffuses out because of the diffusion present in the system. Thus, it closely represents the dynamic behavior observed in a PSA system. Mathematically, Burgers equation is similar to the component mass balance equation of a PSA process, and is written as [115] ∂y +y∂y =μ∂2y, μ=0.01 ∂t ∂x ∂x2 0.5 for 0PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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