A comparative study of two compact finite difference methods: standard vs. mimetic
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hdl:2117/24578
Document typeConference report
Defense date2014
PublisherSociedad Venezolana de Métodos Numéricos en Ingeniería
Rights accessRestricted access - publisher's policy
This work is protected by the corresponding intellectual and industrial property rights.
Except where otherwise noted, its contents are licensed under a Creative Commons license
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Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
In this work, we implement two fourth-order compact finite differences (CFD) methods and use them to model wave propagation on a elastic string. The formulation of the first method employs the standard implicit CFD constructed on nodal grids and requires solving tridiagonal
linear systems at each time iteration. A new second scheme is implemented using the staggered mimetic CFD operators that explicitly approximate derivatives at mid-cell points. The name
mimetic stands for FD operators that satisfy in a discrete sense, some of conservative properties fulfilled by the continuous divergence and gradient operators. Both CFD methods are combined
to high-order Runge-Kutta schemes for time integration. Numerical results show that the mimetic CFD scheme is slightly more accurate but yields similar fourth-order convergence than the nodal
CFD method. In this paper, we also compare the CPU cost of both compact schemes to an explicit Leap-frog staggered solver to show the high computational efficiency of the mimetic CFD scheme.
CitationCórdova, L. [et al.]. A comparative study of two compact finite difference methods: standard vs. mimetic. A: Congreso Internacional de Métodos Numéricos en Ingeniería y Ciencias Aplicadas. "Ingeniería y ciencias aplicadas: modelos matemáticos y computacionales: memorias del XII Congreso Internacional de Métodos Numéricos en Ingeniería y Ciencias Aplicadas: CIMENICS'2014: Isla de Margarita, Venezuela, 24 al 26 de marzo de 2014". Isla de Margarita: Sociedad Venezolana de Métodos Numéricos en Ingeniería, 2014, p. 1-6.
ISBN978-980-7161-04-6
Publisher versionhttp://www.cimenics.org/
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