The need of the aerospace industry, at national or European level, of faster yet reliable computational fluid dynamics models is the main drive for the application of model reduction techniques. This need is linked to the time cost of high-fidelity models, rendering them inefficient for applications like multi-disciplinary optimization. With the goal of testing and applying model reduction to computational fluid dynamics models applicable to lifting surfaces, a bibliographical research covering reduction of nonlinear, dynamic, or steady models was conducted. This established the prevalence of projection and least mean squares methods, which rely on solutions of the original high-fidelity model and their proper orthogonal decomposition to work. Other complementary techniques such as adaptive sampling, greedy sampling, and hybrid models are also presented and discussed. These projection and least mean squares methods are then tested on simple and documented benchmarks to estimate the error and speed-up of the reduced order models thus generated. Dynamic, steady, nonlinear, and multiparametric problems were reduced, with the simplest version of these methods showing the most promise. These methods were later applied to single parameter problems, namely the lid-driven cavity with incompressible Navier–Stokes equations and varying Reynolds number, and the elliptic airfoil at varying angles of attack for compressible Euler flow. An analysis of the performance of these methods is given at the end of this article, highlighting the computational speed-up obtained with these techniques, and the challenges presented by multiparametric problems and problems showing point singularities in their domain.
Second-order fluid dynamics models for travel times in dynamic transportation networks
