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.

翻译：对流主导、间断、移动特征或形状变化问题在计算力学中广泛存在。然而，经典线性模型降阶与插值方法通常无法准确捕捉即使微小的参数变化，导致降阶模型效率低下且精度不足。本文提出一种基于拉东累积分布变换(RCDT)的新型降阶建模方法。研究表明，该非线性变换能显著提升本征正交分解(POD)重构的维度效率，并可精确插值部分对流主导现象。该方法已在多相流体动力学多个算例中得到验证。