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包括固定或移动的边界，两种物理系统都耦合到了。例如，这种情况在非医学和生物学系统中尤为普遍：在人动脉中，血液夫妇的流体动力学与动脉壁的固体动力学，河流和河口在渗透河床中的多孔介质流动。对此类系统的演变进行准确的计算预测仍然是工程师的重要挑战，对相关方法的准确数学分析更加令人生畏。确实，没有已知的方法可以进行严格的数学分析，并且许多方法都遭受稳定或准确性问题，具体取决于界面的方向。数值计算最常在计算网格上执行，这是大量小型构建块中计算域的分解，所谓的元素。我们提出的方法的一个重要特征是，界面可能会通过计算网格的元素进行切割，换句话说，计算网格不需要适合接口。在多物理问题问题上，情况通常是由于计算网格可能不适合界面而需要的，但要适合两个系统的耦合，因此情况通常会变得复杂。这是我们旨在在本项目中研究的情况。新方法将设计用于移动接口上的多物理耦合。数学方法将被设计以使其稳健和准确，我们还将探索将这两个系统分离以进行有效的时间发展的可能性。这可能会导致计算时间中非常重要的节省，特别是对于非线性问题。三个重要的模型案例将被考虑：两种流体的耦合，其中一种或两个都是粘弹性的，自由流和多孔介质流的耦合，最后是流体的耦合以及流体和弹性结构。所有这些应用在人类心血管系统的建模中都有重要的应用，但在其他各种应用中也具有墨水打印机，环境科学，化学工业等的其他应用。