A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics
A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics
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DOI：
10.1098/rspa.2013.0496
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发表时间：
2013-12
期刊：
影响因子：
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通讯作者：
M. Brocchini
中科院分区：
文献类型：
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作者：
M. Brocchini
这篇论文主要是最近一次国际海岸工程会议上关于这一主题的应邀演讲的成果，描述了通过Boussinesq类型模型(BTM)进行建模的最新技术。说明了使用BTMS的动机以及它们的基本原理，特别注意了要描述的物理、所选的模型方程和使用的数值之间的相互作用。分析的视角是物理学家/工程师，而不是应用数学家。给出了目前可用的BTMS从20世纪60年代末的先驱模型开始的时间进度。结合具体的模型和方法，说明了BTMS的主要应用。描述了用于求解BTMS(如有限差分、有限元、有限体积)的数值方法在时间上的演变，特别是对有限体积的关注。最后，概述了目前可用的最重要的BTMS，并说明了需要改进的地方和需要注意的应用领域。
This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention.