Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model
Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model
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DOI：
10.1051/m2an/2014033
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发表时间：
2013-07
期刊：
影响因子：
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通讯作者：
J. Giesselmann;T. Pryer
中科院分区：
文献类型：
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作者：
J. Giesselmann;T. Pryer
我们设计了一个相容的间断Galerkin有限元格式来近似考虑相变的Allen-Cahn/Cahn-Hilliard/Navier-Stokes-Korteweg型准不可压两相流模型。我们证明了该格式是质量守恒的，并且是单调耗能的。在这种情况下，耗散被隔离到已经在连续水平上引起耗散的那些效应的离散等效物，也就是说，没有人为的数值耗散添加到该方案中。在这个意义上，该方法与连续PDE系统的能量耗散是一致的。
We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen–Cahn/Cahn–Hilliard/Navier–Stokes–Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system.