Enhancing CFD predictions in shape design problems by model and parameter space reduction

Abstract

In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

Hull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing

“…Let us initially assume that the input/output relationship of the problem under study is represented by function f (µ) : Ω ⊂ R n → R. The reduction is performed by computing a linear transformation of the original parameters µ M = Aµ, in which A is an M × n matrix, and M < n. In the last years AS has been extended to vector-valued output functions [46], and to nonlinear transformations of the input parameters using the kernel-based active subspaces (KAS) method [48]. AS has been also coupled with reduced order methods such as POD-Galerkin [49] in cardiovascular studies, and POD with interpolation [50] and dynamic mode decomposition [51] for CFD applications. Application to multi-fidelity approximations of scalar functions are also presented in [52,53].…”

Multi‐fidelity data fusion for the approximation of scalar functions with low intrinsic dimensionality through active subspaces

“…Further investigation will involve the use of more active subspaces based fidelities, such as the kernel active subspaces [31]. This could also greatly improve data-driven non-intrusive reduced order methods [40][41][42][43] through modal coefficients reconstruction and prediction for parametric problems. We also mention the possible application to shape optimization problems for the evaluation of both the target function and the constraints.…”

“…Active subspaces (AS) [18,19] can be used to build a surrogate low-fidelity model with reduced input space taking advantage of the correlations of the model's gradients when available. Reduction in parameter space through AS has been proven successful in a diverse range of applications such as: shape optimization [20,21], hydrologic models [22], naval and nautical engineering [23][24][25][26][27], coupled with intrusive reduced order methods in cardiovascular studies [28], in CFD problems in a data-driven setting [29,30]. A kernel-based extension of AS for both scalar and vectorial functions can be found in [31].…”

ATHENA: Advanced Techniques for High dimensional parameter spaces to Enhance Numerical Analysis

“…ATHENA is also utilized in [9] to reduce the dimensionality of a response surface resulting from the shape optimization of an airfoil. The proposed pipeline couples Dynamic Mode Decomposition with Dynamic Active Subspaces to reduce the overall computational resources.…”