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Spatial Discretization Scheme (spatial + discretization_scheme)

Distribution by Scientific Domains
Earth and Environmental Science75%

Selected Abstracts

Performance and numerical behavior of the second-order scheme of precise time-step integration for transient dynamic analysis

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2007
Hang Ma
Abstract Spurious high-frequency responses resulting from spatial discretization in time-step algorithms for structural dynamic analysis have long been an issue of concern in the framework of traditional finite difference methods. Such algorithms should be not only numerically dissipative in a controllable manner, but also unconditionally stable so that the time-step size can be governed solely by the accuracy requirement. In this article, the issue is considered in the framework of the second-order scheme of the precise integration method (PIM). Taking the Newmark-, method as a reference, the performance and numerical behavior of the second-order PIM for elasto-dynamic impact-response problems are studied in detail. In this analysis, the differential quadrature method is used for spatial discretization. The effects of spatial discretization, numerical damping, and time step on solution accuracy are explored by analyzing longitudinal vibrations of a shock-excited rod with rectangular, half-triangular, and Heaviside step impact. Both the analysis and numerical tests show that under the framework of the PIM, the spatial discretization used here can provide a reasonable number of model types for any given error tolerance. In the analysis of dynamic response, an appropriate spatial discretization scheme for a given structure is usually required in order to obtain an accurate and meaningful numerical solution, especially for describing the fine details of traction responses with sharp changes. Under the framework of the PIM, the numerical damping that is often required in traditional integration schemes is found to be unnecessary, and there is no restriction on the size of time steps, because the PIM can usually produce results with machine-like precision and is an unconditionally stable explicit method. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source]

A conservative scheme for the shallow-water system on a staggered geodesic grid based on a Nambu representation

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 639 2009
Matthias Sommer
Abstract A conservative spatial discretization scheme is constructed for a shallow-water system on a geodesic grid with C-type staggering. It is derived from the original equations written in Nambu form, which is a generalization of Hamiltonian representation. The term ,conservative scheme' refers to one that preserves the constitutive quantities, here total energy and potential enstrophy. We give a proof for the non-existence of potential enstrophy sources in this semi-discretization. Furthermore, we show numerically that in comparison with traditional discretizations, such schemes can improve stability and the ability to represent conservation and spectral properties of the underlying partial differential equations. Copyright © 2009 Royal Meteorological Society [source]

Evaluation of three spatial discretization schemes with the Galewsky et al. test

ATMOSPHERIC SCIENCE LETTERS, Issue 3 2010
Seoleun Shin
Abstract We evaluate the Hamiltonian particle methods (HPM) and the Nambu discretization applied to shallow-water equations on the sphere using the test suggested by Galewsky et al. (2004). Both simulations show excellent conservation of energy and are stable in long-term simulation. We repeat the test also using the ICOSWP scheme to compare with the two conservative spatial discretization schemes. The HPM simulation captures the main features of the reference solution, but wave 5 pattern is dominant in the simulations applied on the ICON grid with relatively low spatial resolutions. Nevertheless, agreement in statistics between the three schemes indicates their qualitatively similar behaviors in the long-term integration. Copyright © 2010 Royal Meteorological Society [source]