An immersed discontinuous finite element method for the Stokes problem with a moving interface

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:362

Article; Proceedings Paper

Adjerid, Slimane¹  Chaabane, Nabil¹  Lin, Tao¹  Yue, Pengtao¹ 

[1] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

关键词: Immersed finite element;    Discontinuous Galerkin;    Stokes problem;    Interfacial flow;    Drop deformation;    Surface tension;   

DOI  :  10.1016/j.cam.2018.07.033

来源: Elsevier

【 摘 要 】

We present a discontinuous immersed finite element (IFE) method for incompressible interfacial flows that are governed by the Stokes equations. The method is based on a Cartesian mesh with elements cut by the moving interface. On this fixed unfitted mesh. we employ an immersed Q(1)/Q(0) finite element space constructed according to the location of the interface and pertinent interface jump conditions. As such, the smearing of solution across the interface is greatly reduced. The interface, represented by a sequence of marker points, is advected on the fixed background mesh by the local fluid velocity. The mesh is locally refined near the interface to further improve accuracy. Compared with the phase field method on adaptive meshes, our method can achieve the same level of accuracy with much less degrees of freedoms. We present some numerical examples to validate and demonstrate the capability of the proposed method. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free