Challenges of Residual Minimization-based Model Order Reduction in Car Aerodynamics
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The central enabling methodology for interactive aerodynamic car design with real-time aerodynamic evaluations is Reduced Order Modeling (ROM). In industrial applications, such ROMs mostly rely on the “POD + Interpolation” (POD-I) paradigm (e.g. [1]). While very robust, the accuracy of this approach depends on the formal order of the interpolation scheme and the sampling density. With the aim of more accurate predictions, also in areas of the design space with poor sampling (which is physiological in high dimensional design spaces), we started to implement a Residual Minimization-based ROM [2] adapted to the requirements of interactive aerodynamic car design. While the full-order solution for car aerodynamics is based on time-averaged incompressible Detached-Eddy Simulations (DES), we restricted ourselves for the time being to steady-state incompressible Reynolds-Averaged Navier Stokes (RANS) computations, more precisely with the SIMPLE solver in OpenFOAM®. As our ROM strategy, we chose the steady-state version of the well-known Least Squares Petrov Galerkin approach (LSPG, [3]) which belongs to the family of projection-based model order reduction (pMOR). It guarantees that if the solution can be represented (i.e. in the limit of vanishing projection error) the algorithm will obtain this solution since by definition it exhibits the lowest residuals. The starting point of this work is the empirical evidence that for industrial settings, i.e. for problems with finite but acceptable projection errors, the solution in the reduced space with minimal residual is far from the projected solution. With far we mean at a barycentric distance of the order of the spacing of the sampling. To illustrate this, numerical experiments have been performed on a backward facing step problem, with varying angle of the step (Fig. 1, left column). In the talk, the various implementation aspects and their respective effects on mitigating this shift will be presented along two test cases (Fig. 1): the above-mentioned “minimal” version of the 2D laminar backward facing step and a coarsely meshed 3D Ahmed body.