The Energy Agency of the Republic of Slovenia regulates and determines the operations of the natural-gas market, charges for related gas imbalances, decides on suppliers and controls penalty provisions relating to breaches of stipulated provisions. Each supplier regulates and determines the charges for the differences between the ordered (predicted) and the actually supplied quantities. Store Steel Company is one of the major spring-steel producers in Europe. Its natural gas consumption represents approximately 1.1% of Slovenia’s national natural gas consumption. The company is contractually bound to a supplier which exacts penalties according to the differences mentioned above. A successful approach to gas consumption prediction is elaborated in this paper, with the aim of minimizing associated costs. In the attempt to model and predict the gas consumption and, accordingly, to minimize ordered and supplied gas quantity error, we used linear regression and the genetic programming approach. The genetic programming model performs approximately two times more favourably. The developed gas consumption model has been used in practice since April 2005. The results show good agreement between the model-based ordered quantities and the actually supplied quantities, with savings amounting to approximately 100,000 EUR per year.
COBISS.SI-ID: 3219707
A meshless solution of the recently proposed industrial benchmark test for continuous casting (Šarler et al., 2012) is displayed in the present paper. The physical model is established on a set of macroscopic equations for mass, energy, momentum, turbulent kinetic energy, and dissipation rate in two dimensions. The mixture continuum model is used to treat the solidification system. The mushy zone is modelled as a Darcy porous media with Kozeny–Karman permeability relation, where the morphology of the porous media is modeled by a constant value. The incompressible turbulent flow of the molten steel is described by the Low-Reynolds-Number (LRN) k–ε turbulence model, closed by the Abe–Kondoh–Nagano closure coefficients and damping functions. The numerical method is established on explicit time-stepping, collocation with multiquadrics radial basis functions on non-uniform five-nodded influence domains, and adaptive upwinding technique. The velocity–pressure coupling of the incompressible flow is resolved by the explicit Chorin’s fractional step method. The advantages of the method are its simplicity and efficiency, since no polygonisation is involved, easy adaptation of the nodal points in areas with high gradients, almost the same formulation in two and three dimensions, high accuracy and low numerical diffusion. The results are carefully presented and tabulated, together with the results obtained by ANSYS-Fluent, which would in the future permit straightforward comparison with other numerical approaches as well.
COBISS.SI-ID: 3222523
The purpose of the present paper is to develop a Non-singular Method of Fundamental Solutions (NMFS) for two-dimensional anisotropic linear elasticity problems.The NMFS is based on the classical Method of Fundamental Solutions (MFS) with regularization of the singularities. This is achieved by replacing the concentrated point sources with distributed sources over disks around the singularity, as recently developed for isotropic elasticity problem. In case of the displacement boundary conditions, the values of distributed sources are calculated by a simple numerical procedure, since the closed form solution is not available. In case of traction boundary conditions, the respective desingularized values of the derivatives of the fundamental solution in the coordinate directions, as required in the calculations, are calculated indirectly by considering two reference solutions of the linearly varying simple displacement fields. The feasibility and accuracy of the newly developed method are demonstrated through comparison with MFS solutions and analytical solutions for a spectra of anisotropic plane strain elasticity problems, including bi-material arrangements. NMFS turns out to give similar results as the MFS in all spectra of performed tests. The lack of artificial boundary is particularly advantageous for using NMFS in multi-body problems, where MFS completely fails.
COBISS.SI-ID: 3222779
The purpose of the present paper is to extend the use of a novel meshless Local Radial Basis Function Collocation Method (LRBFCM) for solving the two-dimensional, steady, laminar flow over a backward facing step under the influence of the Lorentz force. The incompressible Navier–Stokes equations are under the influence of predetermined static magnetic field numerically solved on a non-uniform node arrangement. In the numerical procedure, local collocation and Multiquadric Radial Basis Functions (MQRBF) are used on five-nodded subdomains. The coupling between the pressure and the velocity is made by using Fractional Step Method (FSM). The considered problem is calculated for Reynolds numbers (Re) ranging from 300 to 800, Hartman numbers (Ha) ranging from 0 to 100, and for low magnetic Reynolds number (Rem). The numerical results demonstrate excellent agreement with previously published data, obtained with the classical numerical methods, such as Finite Volume Method (FVM) and Finite Element Method (FEM). Simplicity of the numerical implementation, accuracy and the absence of the polygonalisation are the main advantages of the LRBFCM.
COBISS.SI-ID: 3349243
In this paper, a solution of a two-dimensional (2D) Stokes flow problem, subject to Dirichlet and fluid traction boundary conditions, is developed based on the Non-singular Method of Fundamental Solutions (NMFS). The Stokes equation is decomposed into three coupled Laplace equations for modified components of velocity, and pressure. The solution is based on the collocation of boundary conditions at the physical boundary by the fundamental solution of Laplace equation. The singularities are removed by smoothing over on disks around them. The derivatives on the boundary in the singular points are calculated through simple reference solutions. In NMFS no artificial boundary is needed as in the classical Method of Fundamental Solutions (MFS). Numerical examples include driven cavity flow on a square, analytically solvable solution on a circle and channel flow on a rectangle. The accuracy of the results is assessed by comparison with the MFS solution and analytical solutions. The main advantage of the approach is its simple, boundary only meshless character of the computations, and possibility of straightforward extension of the approach to three-dimensional (3D) problems, moving boundary problems and inverse problems.
COBISS.SI-ID: 3547899