Proper orthogonal decomposition of flow-field in non-stationary geometry

• Published in: Journal of computational physics Vol. 311; pp. 329 - 337
• Main Authors: Troshin, Victor, Seifert, Avi, Sidilkover, David, Tadmor, Gilead
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.04.2016
• Subjects: Aero-elasticity; Algorithms; Boundaries; Computational fluid dynamics; Flapping wing flight; Fluid flow; Fluids; Fluid–structure interaction; Laplace equation; Large deformations; Low-order modelling; Mapping; Proper Orthogonal Decomposition; Low-order modelling; Proper orthogonal decomposition; Fluid–structure interaction; Aero-elasticity; Flapping wing flight; Large deformations
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2016.02.006

The current paper outlines a proper orthogonal decomposition (POD) methodology for a flow field in a domain with moving boundaries. In the standard POD approach the properties of the region of the domain, which alternatingly occupied by fluid and solid, are not defined. Here, prior to the decomposition, the domain with moving or deforming boundaries is mapped to a stationary domain using volume preserving mapping. This mapping was created by combining a transfinite interpolation and volume adjustment algorithm. The algorithm is based on an iterative solution of the Laplace equation with respect to the displacement potential of the grid points. Finally the method is demonstrated on CFD results of pitching and plunging ellipse in still fluid. •A method for proper orthogonal decomposition of flow field with moving boundaries is suggested.•The flow-field was mapped to the stationary domain using volume-preserving transformation prior to the POD.•The mapping is a combination of transfinite interpolation and volume adjustment algorithm.•This algorithm is based on the solution of Laplace equation with respect to the displacement potential.•Application of this methodology is demonstrated on CFD data of pitching and plunging ellipse in still fluid.