Implementing multiphysics models in FEniCS: Viscoelastic flows, poroelasticity, and tumor growth

Abstract

The open-source finite element code FEniCS is considered as an alternative to commercial finite element codes for evaluating complex constitutive models of multiphysics phenomena. FEniCS deserves this consideration because it is well-suited for encoding weak forms corresponding to partial differential equations arising from the fundamental balance laws and constitutive equations. It is shown how FEniCS can be adopted for solving boundary-value problems describing viscoelastic flows, poroelasticity, and tumor growth. Those problems span a wide range of models of continuum mechanics, and involve Eulerian, Lagrangian, and combined Eulerian-Lagrangian descriptions. Thus it is demonstrated that FEniCS is a viable computational tool capable of transcending traditional barriers between computational fluid and solid mechanics. Furthermore, it is shown that FEniCS implementations are straightforward, and do not require advanced knowledge of finite element methods and/or coding skills.

Keywords

• FEniCs
• Multiphysics problems
• Viscoelastic flows
• Poroelasticity
• Tumor growth