Numerical modelling of semi-rigid boltless connectors

The paper describes a finite element analysis of a boltless semi-rigid beam-end connector used in the storage rack industry. An elastic three-dimensional linear analysis of the connector was made and the results compared with experiments. The effects of different boundary conditions were investigated. Sub-models of the part of the upright in contact with the connection were made to determine the influence of upright behaviour on the moment–curvature relation. Comparisons with experimental results are made to validate the model. The paper also points out the variation in connection stiffness found by using different measurement positions.     

Numerical modelling of the cold ion-ion hybrid resonance

A new way is discussed to handle numerically the ion-ion hybrid resonance appearing in the cold plasma model for plasma heating in the ion-cyclotron range of frequency (ICRF). It is shown that this singularity can be correctly treated without introducing artificial and unphysical damping outside the resonance domain. This feature is particularly important for computations in two dimensions. This note supplements and corrects a recently published conference contribution [Comput. Phys. Commun. 43 (1986) 125].     

Numerical modelling of fatigue crack initiation of martensitic steel

Numerical simulation of micro-crack initiation that is based on Tanaka–Mura micro-crack nucleation model is presented. Three improvements were added to this model. Firstly, multiple slip bands where micro-cracks may occur are used in each grain. Second improvement deals with micro-crack coalescence by extending existing micro-cracks along grain boundaries and connecting them into a macro-crack. The third improvement handles segmented micro-crack generation, where a micro-crack is not nucleated in one step like in Tanaka–Mura model, but is instead generated in multiple steps. Numerical simulation of crack-initiation was performed with ABAQUS, using a plug-in that was written specially for handling micro-crack nucleation and coalescence. Since numerical model was directed at simulating fatigue properties of thermally cut steel with martensitic structure, edge properties of specimen were additionally inspected in terms of micro-structural properties, surface roughness and residual stresses.     

Numerical methods for modelling leaching of pollutants in soils

Linear equilibrium and non-equilibrium models for leaching of solutes in soils give rise to unsteady linear convection–diffusion–reaction problems. We present several numerical schemes to approximate the solution of this kind of problems based on Stabilized Finite Element Methods, including the recent Link-Cutting Bubbles strategy adapted to deal with unsteady problems, which gives the best numerical results.     

Numerical modelling of a gravity settler in dynamic conditions

An iterative numerical technique has been developed to simulate in detail the dynamics of a shallow-layer gravity settler. Currently acknowledged models apply only to specific equipments at steady-state and laboratory scale [Jeelani SAK, Hartland S. The continuous separation of liquid/liquid dispersions. Chem Eng Sci 1993;48(2):239–54]. To our knowledge, no study has ever addressed the dynamic simulation of a gravity settler. In this paper a direct numerical technique is presented for computing the thickness and drop-size composition of the dispersion band formed in a shallow-layer settler under steady-state and transient conditions. This technique is an extension for the settler of the one used on the stirred vessel by Ribeiro [Ribeiro LM. Simulação Dinâmica de Sistemas Líquido–Líquido, Um novo Algoritmo com Potencialidades de Aplicação em Controlo. PhD thesis, Universidade do Minho, Portugal; 1995].     

Numerical modelling of moving interfaces under local equilibrium conditions

A new method is presented to simulate moving interfaces during diffusion-controlled growth under local equilibrium conditions. The position and compositions of the interface are obtained directly from the equilibrium state of the subsystem around the moving interface, without iterative calculation between diffusion fluxes and solute balance conditions. The method is applicable to general multi-component systems, and it ensures the consistency in compositions and solute balance at the interfaces; Those are ascribed to the presented consideration of subsystem around the interface region in a discretized form. Explicit equations of interface compositions and position in discretized variables are also presented for the simplified ternary systems of two-solution and compound/solution. The validity and usefulness of the method is demonstrated by simulations of the two important ternary systems; The simulation results illustrate the features of diffusion-controlled growth with different alloy compositions and diffusivities of solutes in both systems.     

Numerical modelling of wind flow over a complex topography

Numerical modelling of wind flow over complex dune topography is an ambitious prospect. There is an increasing need to understand wind flow over complex topography for land planning purposes to enable prediction of sediment transport at a particular site. New surveying techniques permit the rapid development of digital terrain models, however a stumbling block is the ability of Computational Fluid Dynamics (CFD) to emulate the wind flow over such a landscape. To overcome these difficulties, it is important to establish the parameters within which such simulations can operate. This paper details an initial two-dimensional numerical model developed in order to test various modelling assumptions against experimental field wind data. Mason Bay, Stewart Island, New Zealand was chosen as an undisturbed but accessible experimental site with a prevalent on-shore wind perpendicular to a simple foredune and a complex down-wind parabolic dune system. A complex topographical two-dimensional model with vegetation represented as a roughness was compared against field data along a transect dissecting a dune system.This paper establishes that:

* Replicating the roughness patterns at the surface is important

* The inlet profile should be duplicated with care

* Modelling only a portion of the domain can have an effect on the flow patterns due to outflow effects

* There is a modelling decision to be made between the complexity of the topography and the sophistication of the turbulence model and degree to which vegetation and sand transportation are modelled.

The long-term aim is to instil confidence in numerical techniques so that such technology can be used for predictive purposes.     

Numerical modelling and passive flow control using porous media

The whole flow over a solid body covered by a porous layer is presented. The three main models used in the literature to compute efficiently the fluid flow are given: the reduction of the porous layer to a boundary condition, the coupling of Darcy equation with Navier-Stokes equations and the Brinkman-Navier-Stokes equations or the penalisation method. Numerical simulations on Cartesian grids using the latest model give easily accurate solutions of the flow around solid bodies with or without porous layers. Adding appropriate porous devices to the solid bodies, an efficient passive control of the two-dimensional incompressible flow is achieved. A strong regularisation of the flow is observed and a significant reduction of the vortex induced vibrations or the drag coefficient is obtained.     

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler–Taylor expansion and stochastic Runge–Kutta type.     

Numerical modelling of trace element fractionation during diffusion controlled crystallization

A FORTRAN IV computer program is presented and described which models the fractionation of trace elements during simple diffusion controlled crystallization of magmas. Two mathematical techniques are used: Crank—Nicolson finite difference and Lanczos tau polynomial methods, because it was determined that there were regions in which either one or the other was unsuitable. The regions of applicability of the respective methods are identified. The program can be used in several manners: (1) It can model diffusion controlled crystallization in which the melt is initially homogeneous in composition, with K (partition coefficient), D (diffusion coefficient), and R (rate of crystal growth) specified. Any of these variables may be changed during crystallization; (2) It can model a situation where the melt has compositional heterogeneity (specified by user), with K, R and D also specified. These variables may be changed during crystallization; (3) If the solid profile is specified, as well as K, the program can be made to calculate best-fit values for R/D ratio. Output from the program compares favourably with actual analytical data from the Bushveld Complex, South Africa. Although the geological basis for the model probably is conceptually simplistic, the model provides a basis for comparison with natural data, and thus can assist in obtaining greater insight into the processes involved in magmatic crystallization.     

Numerical modelling of incompressible flows for Newtonian and non-Newtonian fluids

This paper deals with numerical solution of two-dimensional and three-dimensional steady and unsteady laminar incompressible flows for Newtonian and non-Newtonian shear thickening fluids flow through a branching channel. The mathematical model used in this work is the generalized system of Navier–Stokes equations. The right hand side of this system is defined by the power-law model. The finite volume method combined with artificial compressibility method is used for numerical simulations of generalized Newtonian fluids flow. Numerical solution is divided into two parts, steady state and unsteady. Steady state solution is achieved for t→∞$t\to \infty$ using steady boundary conditions and followed by steady residual behaviour. For unsteady solution high artificial compressibility coefficient β²${\beta }^2$ is considered. An artificial compressibility method with a pulsation of the pressure in the outlet boundary is used.     

Numerical modelling of even-aged plant population dynamics. Two-dimensional model

Vegetation cover. Modelling is in rather wide use when studying plant objects and in the first place their production process. The main attention in it is paid to mathematical modelling on the level of a single plant and a vegetation cover in the whole. As usual, the models of a single plant are of compartmental character and reflect the existing conceptions of variety of the plants life processes. In analysis of cover in the whole the same set of conceptions is directly used, actually considering the cover as one big plant or, to be more exact, as a homogeneous film of plant substance. In this way, a certain part of biological point under consideration is lacking, since in reality the vegetation cover consists of separate interacting plants.     

Numerical modelling of interfacial soil erosion with viscous incompressible flows

The aim of this study is to develop a numerical model for simulating surface erosion occurring at a fluid/soil interface subject to a flow process. Balance equations with jump relations are used. A penalization procedure including a fictitious domain method is used to compute the Stokes flow around obstacles, in order to avoid body-fitted unstructured meshes and instead use fast and efficient finite volume approximations on Cartesian meshes. The evolution of the water/soil interface is described by using a level set function. The ability of the model to predict the interfacial erosion of soils is confirmed by several numerical simulations.     

Numerical modelling of consolidation processes under the water level elevation changes

The paper presents a numerical model of coupled hydro-mechanical behaviour of soils. The micro-mechanics model is based on the effective stress concept which covers the theory of deformation of soils (soil skeleton) and other porous materials. The final set of equations is simplified and derived for the water flow in a porous media and the spatial discretization is performed by the finite element method. The model was implemented to the SIFEL software package and some numerical examples are presented.     

Numerical modelling of the action of acetolactate synthase isozyme II using simplex optimization

This stimulation investigates the dominant mode of action of acetolactate synthase isozyme II. Several models are considered. A variable step size, fourth-order Runge-Kutta-Fehlberg method integrated the coupled sets of stiff nonlinear rate equations using an NEC PowerMate SX personal computer fitted with a 16-MHz, 32-bit 80386/387 Intel co-processor. The Nelder-Mead simplex method optimized rate constants through a nonlinear least squares procedure. An adapted Larsson-Pardue, technique initialized rate parameter sets. In all cases, the simplex procedure converged by minimizing the sum of the squared errors. In addition, several other convergence criteria were simultaneously applied to ensure model integrity and allow valid cross model comparison, the most stringent being that the absolute relative error of each point be less than the experimental error.Models considered included: the classic case proposed by Schloss et al.; a single path concerted mechanism with complete substrate coverage: asymmetric dual path action with an without concerted substrate conversion to desorbed product; and multiple site action of the A₂B₂ dimer with different efficiencies at each. This model optimized all convergence criteria better than any other but subsequent work showed poor inhibitory action.The simplest model which optimized both inhibition and convergence criteria reasonably well had an asymmetric independent dual path action, with the possibility of either direct or indirect production of the desorbed product from the activated substrate complex.     

Numerical modelling of transspectral processes in natural waters: Implications for remote sensing

Based on a previously developed and thoroughly validated hydrooptical model, numerical simulations of the spectral composition of water leaving radiance are presented. These simulations take into account absorption, elastic scattering, water Raman (inelastic) scattering as well as the fluorescence of chlorophyll ( chl ) and dissolved organics ( doc ). The results obtained for forward modelling were also used for the inverse problem: retrieval of water quality parameters from water volume reflectance ( R ) spectra. The Levenberg-Marquardt multivariate optimization procedure was used for this purpose. Unlike water Raman scattering, the chl and doc fluorescence has an impact on R, so the retrieval results can change substantially for waters rich in chl or doc . Suspended minerals ( sm ) suppress both the chl and doc fluorescence influence on R . The retrieval results indicate that chl can be accurately assessed if the concentration of sm is not low and the doc concentration is < 2 mgCl -1 . For waters devoid of doc, the concentration of chl can be accurately retrieved even if the sm concentration is very low. Retrieval errors prove to be strongly dependent on the fluorescence yield value of both chl and doc .     

Numerical modelling and homogenized constitutive law of large deforming fluid saturated heterogeneous solids

In this paper we treat interactions between large deforming solid and fluid media at the microscopic level. This phenomenon is responsible for viscoelastic behaviour observed as the hereditary creep at the macroscopic scale where the material model is described in terms of the homogenized (effective) parameters. The local microscopic and the upscaled global macroscopic problems are derived for the locally periodic porous microstructure with several inclusions. The parallel computational strategy is proposed to solve the local problems associated with specific microstructures evolving in time. On numerical examples using various geometries of the microstructures we demonstrate how the homogenized properties depend on deformation–diffusion processes undergoing in a particular micro-configuration.     

Numerical problems in modelling of collision in sliding systems subjected to seismic excitations

The study addresses collision in sliding systems subjected to seismic excitations. The collision is modelled according to the impact laws of the mechanics of particles using coefficient of restitution to account for energy losses (Newton's hypothesis). An analytical solution in a small time interval after the collision is constructed viewing the sliding velocity. When constructing numerical solutions, it is assumed that the friction force does not change its sign within one step of integration. If at end of the time step, velocity with an opposite sign is calculated, the obtained solution is incorrect, because the result contradicts the accepted constant sign of the friction force during the time step. To avoid these problems expressions are derived for the magnitude of the time step in which a mathematically correct solution will have place. Recommendations are formulated for numerical simulation of collision in sliding systems subjected to seismic excitations. The obtained correct numerical solutions using the Coulomb model are compared with numerical results from the velocity model of friction forces. It is shown that the velocity model provides the possibility to avoid automatically the above numerical problems by use of its correctness condition.