Multiphase flows are described by the multiphase Navier-Stokes equations. Numerically solving these equations is computationally expensive, and performing many simulations for the purpose of design, optimization and uncertainty quantification is often prohibitively expensive. A simplified model, the so-called two-fluid model, can be derived from a spatial averaging process. The averaging process introduces a closure problem, which is represented by unknown friction terms in the two-fluid model. Correctly modeling these friction terms is a long-standing problem in two-fluid model development. In this work we take a new approach, and learn the closure terms in the two-fluid model from a set of unsteady high-fidelity simulations conducted with the open source code Gerris. These form the training data for a neural network. The neural network provides a functional relation between the two-fluid model's resolved quantities and the closure terms, which are added as source terms to the two-fluid model. With the addition of the locally defined interfacial slope as an input to the closure terms, the trained two-fluid model reproduces the dynamic behavior of high fidelity simulations better than the two-fluid model using a conventional set of closure terms.

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ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering
Scientific Computing

Buist, J., Sanderse, B., van Halder, Y., Koren, B., & van Heijst, G. (2019). Machine learning for closure models in multiphase flow applications. In Proceedings of the International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP (pp. 379–399). doi:10.7712/120219.6348.18409