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Computational methods for multiphysics interface problems

多物理场接口问题的计算方法

基本信息

批准号：
EP/J002313/1
负责人：
Erik Burman
金额：
$ 53.59万
依托单位：
University of Sussex
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2012
资助国家：
英国
起止时间：
2012 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FJ002313%2F1
关键词：
Computational methods multiphysics interface problems

项目摘要

Many problems in science and technology includes a fixed or moving boundary over whichtwo different physical systems are coupled. This situation is particularly common in systems inmedicine and biology, for instance: in the human arteries the fluid dynamics of the blood couples to the solid dynamics of the arterial wall, in rivers and estuaries the free flow couples to the porous media flow in the infiltrated river bed. Making accurate computational predictions of the evolution of such systems remains an important challenge for engineers and the accurate mathematical analysis of the associated methods is even more daunting. Indeed no known methods allow for rigorous mathematical analysis and many suffer from problems of stability or accuracy depending on the orientation of the interface. Numerical computations are most often performed on a computational mesh, that is a decomposition of the computational domain in a large number of small building blocks, so called elements. An important feature of the methods that we propose is that the interface may cut through the elements of the computational mesh, or in other words, the computational mesh does not need to fit the interface.In multiphysics problems the situation is often complicated by the fact that the computational mesh may not be adapted to fit the interface, but the coupling of the two systems must take place independent of the mesh. This is the type of situation that we aim to study in the present project. New approaches will be designed for multiphysics couplings over moving interfaces. The mathematical methods will be designed so as to be robust and accurate and we will also explore the possibility to decouple the two systems for efficient time advancement. This may lead to very important savings in computational time, in particular for nonlinear problems.Three important model cases will be considered: the coupling of two fluids of which one or both may be viscoelastic, the coupling of free flow and porous media flow and finally the coupling of a fluid and an elastic structure. All of these applications have important applications in the modeling of the human cardiovascular system, but also in a wide variety of other applications such as ink-jet printers, environmental science, chemical industry and so on.

科学技术中的许多问题都包括一个固定的或移动的边界，在这个边界上，两个不同的物理系统相互耦合。这种情况在医学和生物系统中尤其常见，例如：在人体动脉中，血液的流体动力学与动脉壁的固体动力学相耦合，在河流和河口中，自由流动与渗透河床中的多孔介质流动相耦合。对于工程师来说，对这类系统的演化做出准确的计算预测仍然是一个重要的挑战，而对相关方法进行准确的数学分析更是令人望而生畏。事实上，没有已知的方法允许进行严格的数学分析，而且许多方法都存在稳定性或准确性问题，这取决于界面的方向。数值计算通常是在计算网格上执行的，计算网格是将计算域分解成大量的小构建块，即所谓的元素。我们提出的方法的一个重要特征是界面可能会穿过计算网格的元素，换句话说，计算网格不需要与界面相适应。在多物理问题中，情况往往因为计算网格可能不适合界面而变得复杂，但两个系统的耦合必须独立于网格发生。这就是我们在本项目中旨在研究的情况类型。将为移动界面上的多物理耦合设计新的方法。数学方法的设计将是稳健和准确的，我们还将探索将这两个系统分离的可能性，以有效地推进时间。这将导致非常重要的计算时间的节省，特别是对于非线性问题。将考虑三种重要的模型情况：两种流体的耦合，其中一种或两种可能是粘弹性的，自由流动和多孔介质流动的耦合，最后是流体和弹性结构的耦合。所有这些应用在人体心血管系统的建模中都有重要的应用，但在喷墨打印机、环境科学、化学工业等其他应用中也有广泛的应用。