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Problems with dominant advection, discontinuities, travelling features, orshape variations are widespread in computational mechanics. However, classicallinear model reduction and interpolation methods typically fail to reproduceeven relatively small parameter variations, making the reduced modelsinefficient and inaccurate. This work proposes a model order reduction approachbased on the Radon-Cumulative-Distribution transform (RCDT). We demonstratenumerically that this non-linear transformation can overcome some limitationsof standard proper orthogonal decomposition (POD) reconstructions and iscapable of interpolating accurately some advection-dominated phenomena,although it may introduce artefacts due to the discrete forward and inversetransform. The method is tested on various test cases coming from bothmanufactured examples and fluid dynamics problems.

A reduced-order model for advection-dominated problems based on Radon Cumulative Distribution Transform