Numerical Dispersion (numerical + dispersion)

Distribution by Scientific Domains

Selected Abstracts

Using PHREEQC to Simulate Solute Transport in Fractured Bedrock

GROUND WATER, Issue 4 2007
David S. Lipson
The geochemical computer model PHREEQC can simulate solute transport in fractured bedrock aquifers that can be conceptualized as dual-porosity flow systems subject to one-dimensional advective-dispersive transport in the bedrock fractures and diffusive transport in the bedrock matrix. This article demonstrates how the physical characteristics of such flow systems can be parameterized for use in PHREEQC, it provides a method for minimizing numerical dispersion in PHREEQC simulations, and it compares PHREEQC simulations with results of an analytical solution. The simulations assumed a dual-porosity conceptual model involving advective-reactive-dispersive transport in the mobile zone (bedrock fracture) and diffusive-reactive transport in the immobile zone (bedrock matrix). The results from the PHREEQC dual-porosity transport model that uses a finite-difference approach showed excellent agreement compared with an analytical solution. [source]

Modelling floodplain sedimentation using particle tracking

Ivo Thonon
Abstract Both climate change and river rehabilitation projects induce changes in floodplain sedimentation. Notably along the lower River Rhine, the sediment deposition patterns and rates are subject to change. To assess the magnitude of these changes, we developed the MoCSED model, a floodplain sedimentation model within a geographical information system for the lower Rhine River. We based MoCSED on the ,method of characteristics' (MoC), a particle tracking method that minimizes numerical dispersion. We implemented the MoCSED model in the PCRaster dynamic modelling language. The model input comprises initial suspended sediment concentrations, water levels, flow velocities, and longitudinal and transverse dispersivities. We used a combination of the Krone and Chen concepts to calculate the subsequent sedimentation (SED routine). We compared the model results with sediment trap data for the Bemmel floodplain along the Dutch Waal River during the 2003 inundation. This comparison showed that MoCSED was able to simulate the pattern of sediment deposition. In addition, the model proved to be an improvement in comparison with a conventional raster-based floodplain sedimentation model for the lower River Rhine. In future, MoCSED may serve well to study the impact of a changing discharge regime due to climate change and floodplain rehabilitation plans on deposition of sediments. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Some finite difference methods for a kind of GKdV equations

X. Lai
Abstract In this paper, some finite difference schemes I, II, III and IV, are investigated and compared in solving a kind of mixed problem of generalized Korteweg-de Vries (GKdV) equations especially the relative errors. Both the numerical dispersion and the numerical dissipation are analysed for the constructed difference scheme I. The stability is also obtained for scheme I and the constructed predictor,corrector scheme IV by using a linearized stability method. Other two schemes, II and III, are also included in the comparison among these four schemes for the numerical analysis of different GKdV equations. The results enable one to consider the relative error when dealing with these kinds of GKdV equations. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A spectral-element method for modelling cavitation in transient fluid,structure interaction

M. A. Sprague
Abstract In an underwater-shock environment, cavitation (boiling) occurs as a result of reflection of the shock wave from the free surface and/or wetted structure causing the pressure in the water to fall below its vapour pressure. If the explosion is sufficiently distant from the structure, the motion of the fluid surrounding the structure may be assumed small, which allows linearization of the governing fluid equations. In 1984, Felippa and DeRuntz developed the cavitating acoustic finite-element (CAFE) method for modelling this phenomenon. While their approach is robust, it is too expensive for realistic 3D simulations. In the work reported here, the efficiency and flexibility of the CAFE approach has been substantially improved by: (i) separating the total field into equilibrium, incident, and scattered components, (ii) replacing the bilinear CAFE basis functions with high-order Legendre-polynomial basis functions, which produces a cavitating acoustic spectral element (CASE) formulation, (iii) employing a simple, non-conformal coupling method for the structure and fluid finite-element models, and (iv) introducing structure,fluid time-step subcycling. Field separation provides flexibility, as it admits non-acoustic incident fields that propagate without numerical dispersion. The use of CASE affords a significant reduction in the number of fluid degrees of freedom required to reach a given level of accuracy. The combined use of subcycling and non-conformal coupling affords order-of-magnitude savings in computational effort. These benefits are illustrated with 1D and 3D canonical underwatershock problems. Copyright © 2004 John Wiley & Sons, Ltd. [source]

On the dispersion of a non-orthogonal TLM cell

Zaiqing Li
Abstract The numerical dispersion of a non-orthogonal transmission line matrix (TLM) algorithm is for the first time investigated. First of all, the dispersion relation is derived in the most general possible case. Then, the validation is carried out in the analysis of a simple one-dimensional example. Results show that the theory is in excellent agreement with the numerical simulation. Numerical results concerning various cell shape dispersion characteristics are presented and show some relatively weak numerical dispersion even for rather highly distorted cells. Finally, some indications concerning cell shape selection to minimize the non-orthogonal TLM cell are proposed. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Wideband finite-difference,time-domain beam propagation method

J. J. Lim
Abstract A wide-band finite-difference,time-domain beam propagation method (FD TD-BPM) based on Padé approximants is introduced to improve the bandwidth of the conventional TD-BPM. Numerical dispersion relations for the TD-BPM are derived to demonstrate the increase in bandwidth of the wide-band TD-BPM. The effects of the spatial and time step sizes on the numerical dispersion are also investigated. It is shown that the wide-band TD-BPM is less sensitive to the choice of spatial step size and allows a larger time step size to be used compared to the finite-difference time-domain (FD-TD) method. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 243,247, 2002; Published online in Wiley InterScience ( DOI 10.1002/mop.10428 [source]

An upwind finite volume element method based on quadrilateral meshes for nonlinear convection-diffusion problems

Fu-Zheng Gao
Abstract Considering an upwind finite volume element method based on convex quadrilateral meshes for computing nonlinear convection-diffusion problems, some techniques, such as calculus of variations, commutating operator, and the theory of prior error estimates and techniques, are adopted. Discrete maximum principle and optimal-order error estimates in H1 norm for fully discrete method are derived to determine the errors in the approximate solution. Thus, the well-known problem [(Li et al., Generalized difference methods for differential equations: numerical analysis of finite volume methods, Marcel Dekker, New York, 2000), p 365.] has been solved. Some numerical experiments show that the method is a very effective engineering computing method for avoiding numerical dispersion and nonphysical oscillations. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2009 [source]