First-order system least squares and the energetic variational approach for two-phase flow

JOURNAL OF COMPUTATIONAL PHYSICS

卷:230

Article

Adler, J. H.¹  Brannick, J.¹  Liu, C.¹  Manteuffel, T.²  Zikatanov, L.¹ 

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

关键词: Multiphase flow;    Energetic variational approach;    Algebraic multigrid;    First-order system least squares;    Nested iteration;   

DOI  :  10.1016/j.jcp.2011.05.002

来源: Elsevier

【 摘 要 】

This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen-Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free