曲线网格的半拉格朗日方法

IF 0.3 Q4 MATHEMATICS

Communications in Applied and Industrial Mathematics Pub Date : 2016-09-01 DOI:10.1515/caim-2016-0024

A. Hamiaz, M. Mehrenberger, H. Sellama, E. Sonnendrücker

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引用次数: 6

摘要

摘要研究了曲线网格的半拉格朗日方法。经典的后向半拉格朗日方法[1]保持恒定状态，但不具有质量保守性。然而，即使空间误差很大，对磁场的自然重建也允许至少在时间上有一级质量守恒。用经典的三次样条插值和任意阶次的三次埃尔米特插值进行插值。高奇阶导数重建被证明是三次样条曲线的一个很好的替代，而三次样条曲线在时间步长趋于零时表现不佳。然后描述了沿[2]线的保守半拉格朗日格式;在这里，质量守恒被自动地满足，并且恒定状态在时间上一直保持到一阶。

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The semi-Lagrangian method on curvilinear grids

Abstract We study the semi-Lagrangian method on curvilinear grids. The classical backward semi-Lagrangian method [1] preserves constant states but is not mass conservative. Natural reconstruction of the field permits nevertheless to have at least first order in time conservation of mass, even if the spatial error is large. Interpolation is performed with classical cubic splines and also cubic Hermite interpolation with arbitrary reconstruction order of the derivatives. High odd order reconstruction of the derivatives is shown to be a good ersatz of cubic splines which do not behave very well as time step tends to zero. A conservative semi-Lagrangian scheme along the lines of [2] is then described; here conservation of mass is automatically satisfied and constant states are shown to be preserved up to first order in time.

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来源期刊

Communications in Applied and Industrial Mathematics Mathematics-Applied Mathematics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.