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Dispersion Analysis (dispersion + analysis)

Distribution by Scientific Domains

Engineering	80%

Selected Abstracts

Dispersion analysis of the meshfree radial point interpolation method for the Helmholtz equation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009
Christina Wenterodt
Abstract When numerical methods such as the finite element method (FEM) are used to solve the Helmholtz equation, the solutions suffer from the so-called pollution effect which leads to inaccurate results, especially for high wave numbers. The main reason for this is that the wave number of the numerical solution disagrees with the wave number of the exact solution, which is known as dispersion. In order to obtain admissible results a very high element resolution is necessary and increased computational time and memory capacity are the consequences. In this paper a meshfree method, namely the radial point interpolation method (RPIM), is investigated with respect to the pollution effect in the 2D-case. It is shown that this methodology is able to reduce the dispersion significantly. Two modifications of the RPIM, namely one with polynomial reproduction and another one with a problem-dependent sine/cosine basis, are also described and tested. Numerical experiments are carried out to demonstrate the advantages of the method compared with the FEM. For identical discretizations, the RPIM yields considerably better results than the FEM. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Dispersion analysis of the least-squares finite-element shallow-water system

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003
D. Y. Le Roux
Abstract The frequency or dispersion relation for the least-squares mixed formulation of the shallow-water equations is analysed. We consider the use of different approximation spaces corresponding to co-located and staggered meshes, respectively. The study includes the effect of Coriolis, and the dispersion properties are compared analytically and graphically with those of the mixed Galerkin formulation. Numerical solutions of a test problem to simulate slow Rossby modes illustrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Development of a class of multiple time-stepping schemes for convection,diffusion equations in two dimensions

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2006
R. K. Lin
Abstract In this paper we present a class of semi-discretization finite difference schemes for solving the transient convection,diffusion equation in two dimensions. The distinct feature of these scheme developments is to transform the unsteady convection,diffusion (CD) equation to the inhomogeneous steady convection,diffusion-reaction (CDR) equation after using different time-stepping schemes for the time derivative term. For the sake of saving memory, the alternating direction implicit scheme of Peaceman and Rachford is employed so that all calculations can be carried out within the one-dimensional framework. For the sake of increasing accuracy, the exact solution for the one-dimensional CDR equation is employed in the development of each scheme. Therefore, the numerical error is attributed primarily to the temporal approximation for the one-dimensional problem. Development of the proposed time-stepping schemes is rooted in the Taylor series expansion. All higher-order time derivatives are replaced with spatial derivatives through use of the model differential equation under investigation. Spatial derivatives with orders higher than two are not taken into account for retaining the linear production term in the convection,diffusion-reaction differential system. The proposed schemes with second, third and fourth temporal accuracy orders have been theoretically explored by conducting Fourier and dispersion analyses and numerically validated by solving three test problems with analytic solutions. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Modelling night-time ecosystem respiration by a constrained source optimization method

GLOBAL CHANGE BIOLOGY, Issue 2 2002
Chun-Ta Lai
Abstract One of the main challenges to quantifying ecosystem carbon budgets is properly quantifying the magnitude of night-time ecosystem respiration. Inverse Lagrangian dispersion analysis provides a promising approach to addressing such a problem when measured mean CO2 concentration profiles and nocturnal velocity statistics are available. An inverse method, termed ,Constrained Source Optimization' or CSO, which couples a localized near-field theory (LNF) of turbulent dispersion to respiratory sources, is developed to estimate seasonal and annual components of ecosystem respiration. A key advantage to the proposed method is that the effects of variable leaf area density on flow statistics are explicitly resolved via higher-order closure principles. In CSO, the source distribution was computed after optimizing key physiological parameters to recover the measured mean concentration profile in a least-square fashion. The proposed method was field-tested using 1 year of 30-min mean CO2 concentration and CO2 flux measurements collected within a 17-year-old (in 1999) even-aged loblolly pine (Pinus taeda L.) stand in central North Carolina. Eddy-covariance flux measurements conditioned on large friction velocity, leaf-level porometry and forest-floor respiration chamber measurements were used to assess the performance of the CSO model. The CSO approach produced reasonable estimates of ecosystem respiration, which permits estimation of ecosystem gross primary production when combined with daytime net ecosystem exchange (NEE) measurements. We employed the CSO approach in modelling annual respiration of above-ground plant components (c. 214 g C m,2 year,1) and forest floor (c. 989 g C m,2 year,1) for estimating gross primary production (c. 1800 g C m,2 year,1) with a NEE of c. 605 g C m,2 year,1 for this pine forest ecosystem. We conclude that the CSO approach can utilise routine CO2 concentration profile measurements to corroborate forest carbon balance estimates from eddy-covariance NEE and chamber-based component flux measurements. [source]

TLM models of waves in moving media: refinements and dispersion analysis

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5 2003
William J O'Connor
Abstract Two recent papers about transmission line matrix (TLM) models of waves in moving media used notional diodes to achieve the appropriate direction-dependent wave speeds. Despite the algorithm's demonstrated success, the operation of the diodes might be criticized for being non-physical from a circuit theory perspective. Alternative circuit models are here developed that avoid this objection, being based on wave two-ports and standard circuit theory components. Their operation obeys the same numerical algorithm derived using the diodes, thereby confirming the validity of the original computational scheme. Furthermore these circuits lead more easily to the direction-dependent wave speed expressions and provide exact analytic results for dispersion and attenuation effects, which are here presented and discussed. Copyright © 2003 John Wiley & Sons, Ltd. [source]