عنوان مقاله [English]
Lately, scientific and engineering computations have been receiving detailed attention, in consequence of the improvement in computer hardware. Faster processors, efficient memory modules, and parallel computation techniques have prepared an adequate base for simulation of complex physical phenomena. However, the challenges in performing a simulation of an engineering problem and analyzing the attainable data increase manifold with the level of difficulty in the governing equations. Despite this fact, attempts to challenge these difficulties are inadequate. Numerical simulations yield large sets of data, which may not be useful as an experimental assignment. These data sets not only provide good and deep intuition into the physics of the problem, but also simultaneously assist the assessment and enhancement of various models that are developed for the computations.
In this article, Proper Orthogonal Decomposition (POD) has been used for fast data estimation of flow the field, calculation of aerodynamical coefficients, and inverse aerodynamic design. In this way, two methods have been used for estimation of inviscid compressible flow fields in various regimes, in which both methods are based on combined form of POD. The first extension is a coupling between the POD method and a cubic spline interpolation, as introduced for inviscid flows. The second is essentially a new technique, which has been introduced by the authors for first time. In this method, some additional calibrations (including a kind of re-projection) are needed to achieve more accurate estimations. The outcome of these low order procedures
can predict variations of flow field, due to variations of some effective parameters (e.g., Mach number or angle of attack) with high accuracy and high speed of computation. For the inverse design, we used a combined model, based on POD with the solution of an optimization problem, to obtain the desired surface pressure distribution or to minimize drag coefficient. In this way, two sets of snapshots have been used; an ensemble of flow fields, which may be pressure distribution or any aerodynamic characteristics, and a geometrical ensemble. The low order POD technique is used for computations of relative POD modes and modal coefficients of these ensembles. To solve the coupled optimization problem, an iterative approach has been used to achieve the desired accuracy. Note that the present inverse design approach can be reconstructed for different forms of the objective function. An order reduction manner has been used to find the optimal number of modes for data reconstruction that is a higher resolution of reconstruction which fewer modes for data reconstruction. The obtained results are compared to CFD simulations or exact solution results as reference data. The results show the relatively good accuracy and also the simplicity of the procedure.