Application of Digital Control Theory to Computational Fluid Dynamics

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New methods for computational fluid dynamics through digital control theory are presented. As well known, computational fluid namics consists of two main parts, i. e. (1) generation of computational grid, and (2) numerical scheme to solve the conservation law. In this investigation, new methods for adaptive grid generation through the optimal regulator of digital control are presented, and, moreover, an attempt to make optimal scheme to solve a conservation law numerically. The performance index of linear optimal regulator problem has a strong relation to the characteristics of adaptive grid generation. Paying attention to this point, one quasi-one, and two dimensional Poisson equations are transformed into the statespace form in the first method. The numerical examples of NACA-0012 airfoil flow field show strong clustering of grid lines at shock waves through these three kinds of adaptation. The numerical solution to a conservation law has state-space from of digital control theory. Constructing a performance index by a second norm for the numerical error, feedback gain minimizing this error should be obtained by solving an optimal regulator problem.