Interpolation of Transonic Flows Using a Proper Orthogonal Decomposition Method

Abstract

A proper orthogonal decomposition (POD) method is used to interpolate the flow around an airfoil for various Mach numbers and angles of attack in the transonic regime. POD uses a few numerical simulations, called snapshots, to create eigenfunctions. These eigenfunctions are combined using weighting coefficients to create a new solution for different values of the input parameters. Since POD methods are linear, their interpolation capabilities are quite limited when dealing with flow presenting nonlinearities, such as shocks. In order to improve their performance for cases involving shocks, a new method is proposed using variable fidelity. The main idea is to use POD to interpolate the difference between the CFD solution obtained on two different grids, a coarse one and a fine one. Then, for any new input parameter value, a coarse grid solution is computed using CFD and the POD interpolated difference is added to predict the fine grid solution. This allows some nonlinearities associated with the flow to be introduced. Results for various Mach numbers and angles of attack are compared to full CFD results. The variable fidelity-based POD method shows good improvement over the classical approach.

Multi-fidelity non-intrusive reduced-order modelling based on manifold alignment

“…-Additive correction [27]: The differences between the high-and low-fidelity results are computed, and a correction ROM is trained from the resulting discrepancy fields. High-fidelity predictions are then made by applying the ROM correction over the corresponding solutions generated by the low-fidelity model or a surrogate of it.…”

“…In their work, they extracted an initial POD basis using the high-fidelity solution and then extended this subspace using basis vectors obtained from the low-fidelity solutions. Similarly, Malouin et al [27] computed the difference between the coarse and fine solutions of the flow around an airfoil, then created a ROM of the resulting discrepancy field. A drawback of interpolating all the solutions onto a common grid is the potential introduction of interpolation errors into the results.…”

“…Furthermore, the above datasets all use grids of different sizes, and thus, have inconsistent dimensionality. Other multi-fidelity ROM methods would require a pre-processing step where all the solutions would be mapped onto a common grid, usually the coarser one [25][26][27]. However, with the MA-ROM method, these results are combined into a single model without additional manipulations of the results.…”

Propeller Position Effects over the Pressure and Friction Coefficients over the Wing of an UAV with Distributed Electric Propulsion: A Proper Orthogonal Decomposition Analysis

“…Like the last study, it is easy to find the application of POD in the field of thermal engines [18][19][20], but this method is also used to analyse different aerodynamic problems. These include the interpolation of transonic flows [21], the creation of reduced-order models to characterise aircraft flying at high angles of attack [22], or to generate three-dimensional flow models for supersonic aircraft that significantly reduces the need of computationally-expensive high fidelity simulations [23].…”

Improved Surrogate Modeling using Machine Learning for Industrial Civil Aircraft Aerodynamics

“…Various techniques have been considered to infer the reduced coefficients: spline interpolation [9], Kriging [10], or radial basis functions [11]. Interpolated ROMs are very popular non-intrusive methods, especially for steady and parametric aerodynamic problems [9,[12][13][14][15]. That is the reason why we propose to use them in this paper.…”