Problems with dominant advection, discontinuities, travelling features, or shape variations are widespread in computational mechanics. However, classical linear model reduction and interpolation methods typically fail to reproduce even relatively small parameter variations, making the reduced models inefficient and inaccurate. In this work a novel reduced order modelling approach is proposed based on the Radon-Cumulative-Distribution transform (RCDT). We show that this non-linear transformation can significantly improve the dimensionality of proper orthogonal decomposition (POD) reconstructions and is capable of interpolating accurately some advection-dominated phenomena. The method is tested on various testcases in multiphase fluid dynamics.

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