# Dr. Xingyuan Chen

Work

**Numerical Modeling of Complex Fluid-structure Interaction**

**Motivation**

Viscoelastic fluids include for example polymer melts and solutions. Different from Newtonian fluids which react instantaneously, the response of viscoelastic fluids depends on the deformation history. Mathematical models currently developed for viscoelastic fluids are either nonlinear partial differential equations (PDE), integro-differential equations, or stochastic differential equations. This research concerns mainly the numerical simulation of nonlinear PDE type of viscoelastic models. One of the simplest constitutive models presents the Oldroyd-B model. Despite the simplicity of the constitutive relation, the dynamics that arise in many flows are complicated enough to present a considerable challenge to numerical simulations.

Consequently the fluid-structure interaction (FSI) problem with viscoelastic fluids is a hot topic in recent years. Its application can be widely seen in micro electro mechanical system (MEMS) and biomechanics. Numerical techniques will benefit engineers who use numerical simulations to optimize the production processes. However numerical simulation for this problem is now still a challenge. Understanding the FSI problem and developing an efficient simulation strategy is the goal of this research.

**Research**

The first part of the research is numerical simulation of viscoelastic fluids. In the numerical simulation, one of the challenging problems is the so called ‘High Weissenberg Number Problem (HWNP)’. The Weissenberg Number (Wi) is a dimensionless number, which represents the effect of the elasticity of a fluid. In this research the reason of the HWNP is studied and various approaches to defeat the HWNP are investigated.

The second part and also the main part of the research is numerical simulation of the FSI problem with viscoelastic fluids. Based on the FSI coupling strategy for (generalized) Newtonian fluids, viscoelastic effect of the fluid is taken into account. It is a coupling problem of fluid and structure fields. Implicit partitioned approach is here employed. The fluid part and the structure part are solved separately. The interface between the two fields is the focal point in the investigation.

In the simulation, the fluid part is computed by FASTEST, a finite-volume solver from the Institute Numerical Methods in Mechanical engineering (FNB), TU Darmstadt; the structure part is calculated by the finite-element solver FEAP from University of California, Berkley; the communication between FASTEST and FEAP is realized with MpCCI, a coupling library from Fraunhofer SCAI.

**Preliminary Results**

• Viscoelastic fluid flows in simple geometry domain

• Viscoelastic fluid flows in complex geometry domain

• Viscoelastic fluid flow simulations using various HWNP approaches

• Fluid-structure interaction for generalized Newtonian fluids

**Acknowledgement **

Institute of Numerical Methods in Mechanical Engineering, TU Darmstadt