On Convergent Schemes for Diffuse Interface Models for Two-Phase Flow of Incompressible Fluids with General Mass Densities
On Convergent Schemes for Diffuse Interface Models for Two-Phase Flow of Incompressible Fluids with General Mass Densities
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DOI：
10.1137/130908208
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发表时间：
2013-11
期刊：
影响因子：
--
通讯作者：
G. Grün
中科院分区：
文献类型：
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作者：
G. Grün
我们关注的是[Grun和Klingbeil，J. COMPUT.物理、出版中，DOI：10.1016/j.jcp.2013.10.028]。它们是为[H. Abels，H. Garcke和G. Grun，数学模型方法应用科学，22（2012），1150013]，其描述了不混溶的不可压缩粘性流体的两相流。我们制定一般条件离散空间和投影算子，使我们能够证明紧凑的离散解决方案的时间和空间，从而使我们能够建立一个广义的解决方案的收敛性。我们确定了一个简单的定量和物理标准，以决定是否这个广义解实际上是一个弱解。在这种情况下，我们的分析提供了另一种途径，建立弱解的存在性，上述模型在二维和三维空间。我们的论点特别是基于更高的规律性结果...
We are concerned with convergence results for fully discrete finite-element schemes suggested in [Grun and Klingbeil, J. Comput. Phys., in press, DOI: 10.1016/j.jcp.2013.10.028]. They were developed for the diffuse interface model in [H. Abels, H. Garcke, and G. Grun, Math. Models Methods Appl. Sci., 22 (2012), 1150013], which describes two-phase flow of immiscible, incompressible viscous fluids. We formulate general conditions on discretization spaces and projection operators which allow us to prove compactness of discrete solutions with respect to both time and space and which hence permit us to establish convergence of the scheme to a generalized solution. We identify a simple quantitative and physical criterion to decide whether this generalized solution is in fact a weak solution. In this case, our analysis provides another pathway to establish existence of weak solutions to the aforementioned model in two and in three space dimensions. Our argument is particularly based on higher regularity results ...