A cut finite element method for incompressible two-phase Navier-Stokes flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:384

Article

Frachon, Thomas¹  Zahedi, Sara¹ 

[1] KTH Royal Inst Technol, Dept Math, SE-10044 Stockholm, Sweden

关键词: Unfitted finite element method;    Space-time CutFEM;    Sharp interface method;    Surface tension;    Navier-Stokes;    Level set method;   

DOI  :  10.1016/j.jcp.2019.01.028

来源: Elsevier

【 摘 要 】

We present a space-time Cut Finite Element Method (CutFEM) for the time-dependent Navier-Stokes equations involving two immiscible incompressible fluids with different viscosities, densities, and with surface tension. The numerical method is able to accurately capture the strong discontinuity in the pressure and the weak discontinuity in the velocity field across evolving interfaces without re-meshing processes or regularization of the problem. We combine the strategy proposed in P. Hansbo et al. (2014) [14] for the Stokes equations with a stationary interface and the space-time strategy presented in P. Hansbo et al. (2016) [20]. We also propose a strategy for computing high order approximations of the surface tension force by computing a stabilized mean curvature vector. The presented space-time CutFEM uses a fixed mesh but includes stabilization terms that control the condition number of the resulting system matrix independently of the position of the interface, ensure stability and a convenient implementation of the space-time method based on quadrature in time. Numerical experiments in two and three space dimensions show that the numerical method is able to accurately capture the discontinuities in the pressure and the velocity field across evolving interfaces without requiring the mesh to be conformed to the interface and with good stability properties. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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