Internal wave reflections and transmissions arising from a non‐uniform mesh. Part I: An analysis for the Crank–Nicolson linear finite element scheme
作者:
B. Cathers,
S. Bates,
B. A. O'Connor,
期刊:
International Journal for Numerical Methods in Fluids
(WILEY Available online 1989)
卷期:
Volume 9,
issue 7
页码: 783-810
ISSN:0271-2091
年代: 1989
DOI:10.1002/fld.1650090704
出版商: John Wiley&Sons, Ltd
关键词: Non‐uniform mesh;Wave Reflection/transmission;Crank–Nicolson finite elements;Fourier analysis
数据来源: WILEY
摘要:
AbstractThis is the first of a series of three related papers dealing with some of the consequences of non‐uniform meshes in a numerical model. In this paper the accuracy of the Crank–Nicolson linear finite element scheme, which is applied to the linear shallow water equations, is examined in the context of a single abrupt change in nodal spacing. The (in)accuracy is quantified in terms of reflection and transmission coefficients. An incident wave impinging on the interface between two regions with different nodal spacings is shown to give rise to no reflected waves andtwotransmitted waves. The analysis is verified using three different wavelengths (2Δx, 4Δx8Δx) in three ‘hot‐start’ numerical experiments with a mesh expansion factor of 2 and three experiments with a mesh contraction factor of 1/2. An energy flux analysis based on the concept of group velocity shows that energy is conserved across t
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