Isogeometric Analysis of the Navier–Stokes–Cahn–Hilliard equations with application to incompressible two-phase flows

Babak S. Hosseini; Stefan Turek; Matthias M?ller; Christian Palmes

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Isogeometric Analysis of the Navier–Stokes–Cahn–Hilliard equations with application to incompressible two-phase flows

机译：用施加到不可压缩的两相流量的Navier-Stokes-Cahn-Hilliard方程式的Isogeometric分析

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Abstract

In this work, we provide a unified and comparative description of the most prominent phase field based two-phase flow models and present our numerical results of the application of Galerkin-based Isogeometric Analysis (IGA) to incompressible Navier–Stokes–Cahn–Hilliard (NSCH) equations in velocity–pressure–phase field-chemical potential formulation. For the approximation of the velocity and pressure fields, LBB compatible non-uniform rational B-spline spaces are used which can be regarded as smooth generalizations of Taylor–Hood pairs of finite element spaces. The one-step θ-scheme is used for the discretization in time. The static and rising bubble, in addition to the nonlinear Rayleigh–Taylor instability flow problems, are considered in two dimensions as model problems in order to investigate the numerical properties of the scheme.

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机译：<！[cdata [ Abstract

在这项工作中，我们提供了基于最突出的两相流模型的统一和比较描述，并呈现了我们的数值结果基于Galerkin的异射分析（IgA）在速度 - 压相场 - 化学电位制剂中的不压缩Navier-Stokes-Cahn-Hilliard（NSCH）方程的应用。对于速度和压力场的近似，使用LBB兼容的非均匀RationAtteB样条空间，其可以被视为泰勒罩对有限元空间的平滑推广。一步θ -scheme用于离散化。除了非线性瑞利 - 泰勒不稳定性问题之外，静态和上升气泡在两个维度中被认为是模型问题，以研究方案的数值。 ]]>

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来源
《Journal of Computational Physics》 |2017年第2017期|共24页
作者
Babak S. Hosseini; Stefan Turek; Matthias M?ller; Christian Palmes;
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作者单位

TU Dortmund Institute of Applied Mathematics (LS III);

TU Dortmund Institute of Applied Mathematics (LS III);

Delft University of Technology Delft Institute of Applied Mathematics;

TU Dortmund Institute of Applied Mathematics (LS III);

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原文格式 PDF
正文语种 eng
中图分类数学物理方法;
关键词
Two-phase flow; Cahn–Hilliard phase field model; Navier–Stokes–Cahn–Hilliard equations; Isogeometric analysis; Isogeometric finite elements; B-splines/NURBS; Rising bubble; Rayleigh–Taylor instability;

机译：两相流动;CAHN-HILLIARD期间模型;Navier-Stokes-CAHN-HALLIARD方程;异步测定分析;异诊测量有限元;B样条/ NURBS;上升泡沫;瑞利 - 泰勒不稳定;

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专利

1. Isogeometric Analysis of the Navier–Stokes–Cahn–Hilliard equations with application to incompressible two-phase flows [J] . Babak S. Hosseini, Stefan Turek, Matthias M?ller, Journal of Computational Physics . 2017,第期

机译：用施加到不可压缩的两相流量的Navier-Stokes-Cahn-Hilliard方程式的Isogeometric分析
2. Instability of two-phase flows: A lower bound on the dimension of the global attractor of the Cahn-Hilliard-Navier-Stokes system [J] . Gal C.G., Grasselli M. Physica, D. Nonlinear phenomena . 2011,第7期

机译：两相流的不稳定性：Cahn-Hilliard-Navier-Stokes系统的全局吸引子的维数下限
3. Fully discrete finite element approximations of the Navier-Stokes-Cahn-Hilliard diffuse interface model for two-phase fluid flows [J] . Feng XB SIAM Journal on Numerical Analysis . 2006,第3期

机译：两相流体流动的Navier-Stokes-Cahn-Hilliard扩散界面模型的完全离散有限元逼近
4. A Nonlinear Model Predictive Concept for Control of Two-Phase Flows Governed by the Cahn-Hilliard Navier-Stokes System [C] . Michael Hinze, Christian Kahle IFIP TC 7 conference on system modeling and optimization . 2013

机译：Cahn-Hilliard Navier-Stokes系统控制的两相流控制的非线性模型预测概念
5. 2-D, 3-D and 4-D anisotropic mesh adaptation for the time-continuous space-time finite element method with applications to the incompressible Navier-Stokes equations. [D] . Tremblay, Pascal. 2008

机译：2D，3D和4D各向异性网格自适应，适用于时间连续的时空有限元方法，并适用于不可压缩的Navier-Stokes方程。
6. Particles at fluid-fluid interfaces: A new Navier-Stokes-Cahn-Hilliard surface-phase-field-crystal model [O] . Sebastian Aland, John Lowengrub, Axel Voigt -1

机译：在流体 - 流体界面的颗粒：一种新的Navier-stokes-的Cahn-Hilliard的表面相场晶模型
7. Isogeometric Analysis of the Navier-Stokes-Cahn-Hilliard equations with application to incompressible two-phase flows [O] . Hosseini Babak S., Turek Stefan, Möller Matthias, 2016

机译：Navier-Stokes-Cahn-Hilliard方程的等几何分析及其在不可压缩两相流中的应用
8. Comparative Analysis of Natural Convection Flows Simulated by Both the Conservation and Incompressible Forms of the Navier-Stokes Equations in a Differentially-Heated Square Cavity [R] . Martineau, R. C., Berry, R. A., Esteve, A., 2009

机译：差热平方腔中Navier-stokes方程的守恒和不可压缩形式模拟自然对流的对比分析

Isogeometric Analysis of the Navier–Stokes–Cahn–Hilliard equations with application to incompressible two-phase flows

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