Compression of aerodynamic databases using high-order singular value decomposition

A methodology based on high-order singular value decomposition is presented to compress multidimensional (with the various dimensions associated with both the spatial coordinates and parameter values) aerodynamic databases. The method is illustrated with a database containing computational fluid dynamics calculations of the outer flow around a wing, with two free parameters, the Mach number and the angle of attack. Comparison is made between the results of compressing just one flow snapshot (for fixed values of the parameters), compressing a one-parameter family of snapshots, and compressing the whole database. Several compressing strategies are also discussed that deal with (a) treating the flow variables separately or considering all flow variables at a time, (b) considering the whole flow domain simultaneously or dividing it into blocks, and (c) using various measures of errors. The main conclusion is that a large compression factor is generally obtained. Furthermore, the compression factor increases exponentially as the dimension of the database increases for any fixed error, namely the compression factor increases by an order of magnitude with each new database dimension for an error level of 1%.