NATIONAL TECHNICAL UNIVERSITY OF ATHENS (NTUA) SCHOOL OF MECHANICAL ENGINEERING LAB. OF THERMAL TURBOMACHINES PARALLEL CFD & OPTIMIZATION UNIT (PCOpt) Kyriakos C. Giannakoglou, Professor

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The Parallel CFD & Optimization Unit (PCOpt) of the Lab. of Thermal Turbomachines, Fluids Dept. of the School of Mech. Engineering of NTUA (Prof. K.C. Giannakoglou) develops CFD-based analysis and optimization methods; the latter are used to solve aero/hydrodynamic shape, topology and flow control optimization problems. Developed optimization methods include gradient-free (stochastic) and gradient-based methods coupled with the adjoint approach. The research activities can be summarized as:

• Development and Validation of CFD Analysis Tools
  At PCOpt/NTUA CFD analysis s/w is available both in the OpenFOAM® environment and as in-house tools. The in-house s/w includes both body-fitted and immersed boundary methods. The body-fitted GPU-enabled RANS solver may predict incompressible up to transonic flows. Runs on NVIDIA GPUs by making use of the CUDA parallel computing architecture, with a noticeable speed-up compared to the corresponding CPU code which is also available. Regarding immersed boundary methods, both the Cut-Cell and the Ghost-Cell method for applying the boundary conditions on the non-body-fitted Cartesian mesh are available.
• Development of Evolutionary Algorithms
  Regarding gradient-free optimization (stochastic, population-based), current research focuses on the further development of the generic optimization platform EASY (Evolutionary Algorithm SYstem), developed and brought to market by the PCOpt/NTUA in 2000. EASY is based on multilevel, distributed, metamodel-assisted EAs and can handle single- and multi-objective constrained problems by pluging in any evaluation s/w as black-box (including computationally demanding evaluation CFD etc. tools). For use in real-world applications with many design variables, techniques for dimensionality reduction (such as principal component analysis) are optionally employed. EASY is used by other academic groups and companies in a variety of applications. The following text is a more detailed description of EASY and its capabilities.
• Development of Adjoint Methods
  In the context of gradient-based optimization, continuous (occasionally, discrete too) adjoint methods are developed. The relevant research has led to new continuous adjoint formulations (for example the Think-Discrete Do-Continuous adjoint) for the computation of first-, second- (required by any "exact" Newton method or Uncertainty Quantification) and third-order (for solving design problems under uncertainties based on the method of moments) sensitivity derivatives. The developed adjoint methods are both OpenFOAM-based and based on the in-house GPU-enabled RANS solver, for a variety of objective and constraint functions. Over and above to the TDDC adjoint the following novel contributions can be reported: (a) new, exact continuous adjoint methods for the most widely used one- and two-equation turbulence models; the usual assumption of neglecting turbulence variations ("frozen turbulence" adjoint) which often leads to wrongly signed sensitivity derivatives misleading the optimization algorithm is thus avoided, (b) a new continuous adjoint method for RANS models based on wall functions, which is a great value for car industry applications and (c) a new continuous adjoint formulation which, for the first time, takes into account grid sensitivities and thus computes the exact gradient of the objective function with minimal computational cost. Apart from shape and topology optimization, the optimization of active flow control systems (via steady and pulsating jets) is also carried out using the developed methods. More details on this topic can be found here.
  
• Uncertainty Quantification (UQ) and Robust Design (RD)
  UQ and RD techniques are also developed based on the above tools. Regarding UQ, apart from the Method of Moments (MoM), which profits of the capability of computing high-order sensitivities at low cost (see above), Intrusive and Non-Intrusive Polynomial Chaos Expansion methods have been developed, both based on the in-house RANS solver and OpenFOAM.
• Mesh Morphing Techniques
  Next to the above methods, various grid displacement techniques (Laplacian models, models using linear and torsional springs, RBF models, volumetric NURBS, harmonic coordinates, Delaunay triangulation based, etc) are available to support the optimization loop and avoid remeshing; some of the above tools are also used as morphing techniques.

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