A variable-fidelity aerodynamic model using proper orthogonal decomposition

Abstract

A variable-fidelity aerodynamic model based on proper orthogonal decomposition (POD) of an ensemble of computational fluid dynamics (CFD) solutions at different parameters is presented in this article. The ensemble of CFD solutions consists of two subsets of numerical solutions or snapshots computed at two different nominal orders of accuracy or discretization. These two subsets are referred to as the low-fidelity and high-fidelity solutions or data, whereby the low fidelity corresponds with computations made at the lower nominal order of accuracy or coarser discretization. In this model, the relatively inexpensive low-fidelity data and the more accurate but expensive high-fidelity data are considered altogether to devise an efficient prediction methodology involving as few high-fidelity analyses as possible, while obtaining the desired level of detail and accuracy. The POD of this set of variable-fidelity data produces an optimal linear set of orthogonal basis vectors that best describe the ensemble of numerical solutions altogether. These solutions are projected onto this set of basis vectors to provide a finite set of scalar coefficients that represent either the low-fidelity or high-fidelity solutions. Subsequently, a global response surface is constructed through this set of projection coefficients for each basis vector, which allows predictions to be made at parameter combinations not in the original set of observations. This approach is used to predict supersonic flow over a slender configuration using Navier–Stokes solutions that are computed at two different levels of nominal accuracy as the low-fidelity and high-fidelity solutions. The numerical examples show that the proposed model is efficient and sufficiently accurate.