Discrete Numerical Method Research Articles

A 3D discrete numerical elastic lattice method for seismic wave propagation in heterogeneous media with topography

A three‐dimensional elastic lattice method for the simulation of seismic waves is presented. The model consists of particles arranged on a cubic lattice which interact through a central force term and a bond‐bending force. Particle disturbances are followed through space by numerically solving their equations of motion. A vacuum free‐surface boundary condition is implicit in the method. We demonstrate that a numerical implementation of the method is capable of modelling seismic wave propagation with complex topography. This is achieved by comparing the scheme against a finite‐difference solution to the elastodynamic wave equation. The results indicate that the scheme offers an alternative 3D method for modelling wave propagation in the presence of strong topography and subsurface heterogeneity. We apply the method to seismic wave propagation on Mount Etna to illustrate its applicability in modelling a physical system.

Simulation of the mechanical behavior of inclined jointed rock masses during tunnel construction using Discontinuous Deformation Analysis (DDA)

In this paper, the mechanical behavior of inclined jointed rock masses during tunneling is considered. Such rock masses can be considered as an assembly of discrete blocks with the discontinuities having a significant influence on the mechanical behavior. To simulate this situation, a discrete numerical analysis method, Discontinuous Deformation Analysis (DDA), is applied. The DDA results show the existence of stress arching in the rock masses during tunneling. This stress arching is the primary influence on the stress distribution and surface subsidence. In addition, the stress arching is affected by the dip angle of the jointed rock masses. Moreover, the DDA results are in good agreement with experiments, explaining the reason for the asymmetrical vertical stress and surface subsidence obtained in laboratory tests. These results suggest that DDA can be applied to model the tunneling behavior of complicated discontinuous rock masses.

Continuous integration congestion cost allocation based on sensitivity

Congestion cost allocation is a very important topic in congestion management. Allocation methods based on the Aumann-Shapley value use the discrete numerical integration method which needs to solve the incremented OPF solution many times and as such it is not suitable for practical application to large-scale systems. The optimal solution and its sensitivity change tendency during congestion removal using a DC optimal power flow (OPF) process is analysed. A simple continuous integration method based on the sensitivity is proposed for the congestion cost allocation. The proposed sensitivity analysis method needs a smaller computation time than the method based on using the quadratic method and inner point iteration. The proposed congestion cost allocation method uses a continuous integration method rather than discrete numerical integration. The method does not need to solve the incremented OPF solutions; which allows it use in large-scale systems. The method can also be used for AC OPF congestion management.

Higher-order modeling of continua by finite-element, boundary-element, meshless, and wavelet methods

This paper is an overview of the higher-order modeling schemes for the continua based on finite-element, boundary-element, meshless, and wavelet methods. The first discrete numerical method is well established, so discussions are mainly focused on the last three methods. Apart from critically discussing the main theoretical, algorithmic, and implementation characteristics of the methods, the paper expounds on the relative merits and demerits of the methods. The results of a number of smooth and nonsmooth problems are presented. Finally, the future potential of the wavelet method in discrete numerical modeling of continua is explored.

Modélisation des écoulements granulaires par automates cellulaires

A discrete numerical method based on a cellular automaton may be considered for granular material modelling. First, this paper presents the basics of such a tool: space discretisation in a regular ...

A Fully Discrete BEM-FEM for the Exterior Stokes Problem in the Plane

We reformulate the Johnson--Nedelec approach for the exterior two-dimensional Stokes problem taking advantage of the parameterization of the artificial boundary. The main aim of this paper is the presentation and analysis of a fully discrete numerical method for this problem. This one responds to the needs of having efficient approximate quadratures for the weakly singular boundary integrals. We give a complete error analysis of both the Galerkin and fully discrete Galerkin methods.

離散的数値計算法による音響放射率測定法の実験検討

In the preceding paper the discrete numerical calculation method of sound radiation efficiency has been newly presented and that utility was confirmed. This method is utilized as not only a calculation method but also a measurement method of sound radiation. This is a hybrid method consisting of a measurement of vibration and a calculation of both self- and mutual-radiation impedance. In the present paper, application properties and accuracy of this method are concretely certified in an experiment on sound radiation. As results of the work, the followings are revealed. 1) The discrete numerical calculation method has a lot of merits that a conventional method doesn't possess. 2) The length of imaginary divided part, that is, a space of measurement points, is enough to be half of the bending wave-length at the coincidence frequency.

Nonstandard methods for the convective transport equation with nonlinear reactions

A new nonstandard Lagrangian method is constructed for the one-dimensional, transient convective transport equation with nonlinear reaction terms. An “exact” time-stepping scheme is developed with zero local truncation error with respect to time. The scheme is based on nonlocal treatment of nonlinear reactions, and when applied at each spatial grid point gives the new fully discrete numerical method. This approach leads to solutions free from the numerical instabilities that arise because of incorrect modeling of derivatives and nonlinear reaction terms. Algorithms are developed that preserve the properties of the numerical solution in the case of variable velocity fields by using nonuniform spatial grids. Effects of different interpolation techniques are examined and numerical results are presented to demonstrate the performance of the proposed new method. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 467–485, 1998

Smoothing the solutions of history-dependent dynamical systems

We introduce and analyze a fully discrete numerical method for solving second order integrodifferential equations modelling dynamical systems whose evolution depends also on the past states. We show it is fourth order convergent. Then from the numerical approximate values for the unknown function, we reconstruct by means of deficient quartic splines a smooth solution of the problem. The reconstruction scheme is shown to be cubically convergent. Both methods when assuming analytic evaluation of the integrals are convergent with superquartic and supercubical rates respectively. For ordinary differential equations the scheme for the calculation of the solution at the grid knots gains one order of convergence. Numerical experiments confirm our theoretical findings.

A Quasimolecular Approach for Discrete Study of Droplet Collision

A discrete numerical method based on a molecular approach has been used as an alternative technique for the study of liquid drop dynamics. The Weber number and the Impact number are found to be the key parameters that determine the outcome of collision of two liquid droplets. This study confirms the experimental fact that the number of daughter droplets resulting from the collision of two droplets increases with the Impact number for a large Weber number. The shapes of the droplets at different phases during collision are in accord with the experimental observation.

Stable Numerical Boundary Conditions for Stokes Equations

The author works with the vorticity-stream function formulation of the Stokes equations. Two boundary conditions are given for the stream function while no boundary conditions are given for the vorticity. A derived boundary condition for the vorticity is considered and it is proven that the resulting fully discrete numerical method is stable. The results are then extended to the three-dimensional Stokes equations using a staggered grid.

Simulations for the transient properties of multi-mode delay-line controlled oscillators

This paper describes a discrete time domain numerical simulation method for multi-mode delay-line controlled oscillators, which can yield solutions to both transitent and steady state properties. A new efTicient algorithm for numerical simulations of non-dispersive dealy-lines is given. Experimental results supporting the validity of the theory are also presented.

A vortex-lattice method in the linear theory on a two-dimensional supercavitating flat plate foil

Abstract The vortex-lattice method has been found very satisfactory in the case of steady subsonic wing theory, however, the discrete numerical methods, such as the vortex-lattice method, have not been studied in detail for supercavitating flows. One of the discrete numerical method, a vortex-lattice method, is developed in the present paper for cavitating flows around a two dimensional flat plate foil. The governing equations in the linear theory are represented as a set of coupled integral equations with Cauchy kernel, and there are unknown functions which are not under integral signs. For solving them, they are exchanged to an alternative set of coupled integral equations by a new variable, and the present vortex-lattice method is schemed for equal spacing of the vortices and sources in this new variable. The position of the collocation points is determined, and it is sufficient to treat unknown functions which are not integral signs as step functions. Moreover, the proof of the convergence of this method is shown and the accuracy is estimated.

Pumping-test analysis using a discrete time-discrete space numerical method

The application of a digital computer model of radial flow in an aquifer to the estimation of aquifer parameters is considered. Pumping-test data for a shallow unconfined gravel aquifer, in which the drawdown recorded at the pumped well is a significant proportion of the thickness of the aquifer, are used to test the method. The model is sufficiently flexible to allow for decrease in the saturated thickness, vertical components of flow, well losses and variations of aquifer parameters in time and space.

Discrete Ordinates Numerical Integration Method for Neutron Transport Equation in Slab Geometry

A method is presented for solving neutron transport problems in slab geometry with the application of discrete ordinates numerical integration to the Boltzmann transport equation. Neutron spectra for water, iron and carbon layers are calculated and compared with experimental data. Good agreement is obtained between computed and measured values for both angular distributions and the energy spectra of neutrons. The calculated neutron spectra in an iron-water layer are also presented as an example of solutions derivable for neutron transport problems in multi-layered shield.

Discrete Ordinates Numerical Integration Method for Neutron Transport Equation in Slab Geometry

A method is presented for solving neutron transport problems in slab geometry with the application of discrete ordinates numerical integration to the Boltzmann transport equation. Neutron spectra for water, iron and carbon layers are calculated and compared with experimental data. Good agreement is obtained between computed and measured values for both angular distributions and the energy spectra of neutrons. The calculated neutron spectra in an iron-water layer are also presented as an example of solutions derivable for neutron transport problems in multi-layered shield.