Modeling hyperelasticity in non-equilibrium multiphase flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:330

Article

Hank, Sarah¹  Favrie, Nicolas¹  Massoni, Jacques¹ 

[1] Aix Marseille Univ, CNRS, IUSTI, 5 Rue E Fermi, F-13453 Marseille 13, France

关键词: Hyperelasticity;    Multiphase Flows;    Fluid Structure Interaction;    High Velocity Impact;    Discrete Equation Method;    Godunov type method;   

DOI  :  10.1016/j.jcp.2016.11.001

来源: Elsevier

【 摘 要 】

The aim of this article is the construction of a multiphase hyperelastic model. The Eulerian formulation of the hyperelasticity represents a system of 14 conservative partial differential equations submitted to stationary differential constraints. This model is constructed with an elegant approach where the specific energy is given in separable form. The system admits 14 eigenvalues with 7 characteristic eigenfields. The associated Riemann problem is not easy to solve because of the presence of 7 waves. The shear waves are very diffusive when dealing with the full system. In this paper, we use a splitting approach to solve the whole system using 3 sub-systems. This method reduces the diffusion of the shear waves while allowing to use a classical approximate Riemann solver. The multiphase model is obtained by adapting the discrete equations method. This approach involves an additional equation governing the evolution of a phase function relative to the presence of a phase in a cell. The system is integrated over a multiphase volume control. Finally, each phase admits its own equations system composed of three sub-systems. One and three dimensional test cases are presented. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free