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We develop three reliable iterative methods for solving the nonlinear 1D, 2D and 3D second-order wave equation and compare the results with a discretization-based solver. The iterative Tamimi–Ansari method (TAM), Daftardar–Jafari method (DJM) and the Banach contraction method (BCM) are used to obtain the exact solution for linear equations. For nonlinear equations and practical problems, however, one obtains the approximate solutions that converge to the exact solution, if one exists. The convergence analysis of the three methods is shown using the fixed-point theorem. The methods prove to be quite efficient and well suited to solve this kind of problems. We present several examples that demonstrate the accuracy and efficiency of the methods. We also compare the methods with a method based on discretization (Boundary Domain Integral Method (BDIM)). The BDIM uses a standard domain grid and discretizes the integral form of the governing equations. The iterative methods were developed with Mathematica® 10, while BDIM is a proprietary development. [ABSTRACT FROM AUTHOR]

In this paper we present the development of numerical methods for two problems in chemical engineering: adsorption of carbon dioxide into phenyl glycidyl ether and diffusion and reaction processes in a porous catalyst. Both problems are modelled by systems of two coupled nonlinear ordinary differential equations. Dirichlet and Neumann type boundary conditions are considered. We develop the standard homotopy analysis method and the boundary-domain element method to solve for the unknown steady-state concentrations of reactants. The validity of the proposed methods is checked and demonstrated by numerical examples. Convergence rates are compared and the advantages and drawbacks of the proposed methods are discussed and compared to the Mathematica NDSOLVE solver. We show, that the proposed homotopy analysis method features exponential convergence rate and is highly accurate and efficient. As low as 6 terms are needed to reach error norms of 10 − 5 . Furthermore, the boundary-domain integral approach is also capable of solving the same problem very efficiently, using a very coarse computational mesh (21 nodes). [ABSTRACT FROM AUTHOR]

The paper reports on the development of unique standard gas consumption profiles for the end gas consumers and the preparation of a method for the implementation of the developed profiles for forecasting and preliminary gas allocation. Four years of gas consumption and temperature measurements were used to develop eight types of consumption profiles for 17 gas consumer groups, which were grouped according to their professional activity. As an alternative to the exponential, Gompertz or logistic model functions, frequently used in gas consumption model developments, the sigmoid model function is implemented and model constants for the eight types of profiles are developed based on the knowledge of the temperature independent portion of the gas consumption and separate treatment of workdays/weekends. Based on these profiles, a method was developed for the preliminary allocation of the gas consumption. The developed profiles and the gas consumption allocation method were validated on the available set of gas consumption data for the Slovenian gas market, proving the sigmoid model function based gas consumption allocation as an accurate and viable means of gas consumption forecasting. • Unique standard gas consumption profiles are developed. • A method for usage of the profiles for preliminary allocation is developed. • We provide a way to fairly and in a standard way allocate gas consumption. • The data needed to set up the consumption profiles is attached. [ABSTRACT FROM AUTHOR]

This paper deals primarily with the sedimentation of magnetic microparticles in the presence of an external magnetic field. Based on the analysis of raster images, taken during sedimentation process under the influence of magnetic field, the development of settling velocities occurring as a result of increasing magnetic force is measured. Basics of the magnetic field calculation of a disc neodymium permanent magnet are explained. Numerical particle tracking and particle size determination via image analysis is presented. On the basis of force balance equations for Lagrangian particle tracking and results of experimental tracking of particle positions during sedimentation with magnetic field turned on as well as off, the magnetic susceptibility of microparticles is determined. [ABSTRACT FROM AUTHOR]

A numerical study of particle motion in a cubic lid driven cavity is presented. As a computational tool, a boundary element based flow solver with a Lagrangian particle tracking algorithm is derived. Flow simulations were performed using an in-house boundary element based 3D viscous flow solver. The Lagrangian particle tracking algorithm is capable of simulation of dilute suspensions of particles in viscous flows taking into account gravity, buoyancy, drag, pressure gradient and added mass. The derived algorithm is used to simulate particle behaviour in a cellular flow field and in a lid driven cavity flow. Simulations of particle movement in a cellular flow field were used to validate the algorithm. The main goal of the paper was to numerically simulate the flow behaviour of spheres of different densities and different diameters, as experimentally observed in work of Tsorng et al. The study of slightly buoyant and non-buoyant particles in a lid driven cavity was aimed at discovering cases when particles leave the primary vortex and enter into secondary vortices, a phenomenon described in the work of Tsorng et al. A parametric study of this phenomenon was preformed. The presented computational results show excellent agreement with experiments, confirming the accuracy of the developed computational method. [ABSTRACT FROM AUTHOR]

A numerical model of particle motion in fluid flow under the influence of hydrodynamic and magnetic forces is presented. The Lagrangian particle tracking algorithm was developed being capable of simulating dilute suspensions of particles in viscous flows where gravity, buoyancy, drag, pressure gradient, added mass and magnetophoretic forces are taken into account. The method is used to study the behaviour of magnetite particles in a periodic cellular flow field under the influence of a magnetic field produced by electric wires placed in cell centres. For such a flow field it is known that particles in steady state merge into individual trajectories. The influence of the magnetic field on the particle trajectories is examined and an exponential model for the time evolution of the fraction of adhered particles to the electric wires is proposed. Three particle Stokes number values are considered: 0.01, 0.1 and 1. The existence of a critical magnetic pressure coefficient was found, at which all particles end up to be adhered to the wires. The critical magnetic pressure coefficient was found to be proportional to the Stokes number. For sub-critical magnetic pressure coefficient, the particle trajectories are significantly altered by the magnetic field, both in their shape and in their number. Furthermore, in the sub-critical regime, the minimal distance of particles to the cell centres is larger for particles with smaller Stokes numbers. [ABSTRACT FROM AUTHOR]