**Juan Luis Prieto**

Escuela Técnica Superior de Ingenieros Industriales, Departamento de Ingeniería Energética, Universidad Politécnica de Madrid, José Gutiérrez Abascal 2, 28006 Madrid, Spain; juanluis.prieto@upm.es

Received: 1 July 2020; Accepted: 21 July 2020; Published: 25 July 2020

**Abstract:** This paper presents a numerical study of the viscoelastic effects on drop deformation under two configurations of interest: steady shear flow and complex flow under gravitational effects. We use a finite element method along with Brownian dynamics simulation techniques that avoid the use of closed-form, constitutive equations for the "micro-"scale, studying the viscoelastic effects on drop deformation using an interface capturing technique. The method can be enhanced with a variance-reduced approach to the stochastic modeling, along with machine learning techniques to reconstruct the shape of the polymer stress tensor in complex problems where deformations can be dramatic. The results highlight the effects of viscoelasticity on shape, the polymer stress tensor, and flow streamlines under the analyzed configurations.

**Keywords:** drop; finite element method; machine learning; multiphase flow; particle level set; non-Newtonian fluid
