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
Purpose: The purpose of this work is to upgrade our previous developments of Local Radial Basis Function Collocation Method (LRBFCM) for heat transfer, fluid flow, and electromagnetic problems to thermoelastic problems and to study its numerical performance with the aim to build a multiphysics meshless computing environment based on LRBFCM. Design/methodology/approach: Linear thermoelastic problems for homogenous isotropic body in two dimensions are considered. The stationary stress equilibrium equation is written in terms of deformation field. The domain and boundary can be discretized with arbitrary positioned nodes where the solution is sought. Each of the nodes has its influence domain, encompassing at least six neighboring nodes. The unknown displacement field is collocated on local influence domain nodes with shape functions that consist of a linear combination of multiquadric radial basis functions and monomials. The boundary conditions are analytically satisfied on the influence domains which contain boundary points. The action of the stationary stress equilibrium equation on the constructed interpolation results in a sparse system of linear equations for solution of the displacement field. Findings: The performance of the method is demonstrated on three numerical examples: bending of a square, thermal expansion of a square and thermal expansion of a thick cylinder. Error is observed to be composed of two contributions, one proportional to a power of internodal spacing and the other to a power of the shape parameter. The latter term is the reason for the observed accuracy saturation, while the former term describes the order of convergence. The explanation of the observed error is given for the smallest number of collocation points (six) used in local domain of influence. The observed error behavior is explained by considering the Taylor series expansion of the interpolant. The method can achieve high accuracy and performs well for the examples considered. Originality: LRBFCM has been developed for thermoelasticity and its error behaviour studied. A robust way of controlling the error was devised from consideration of the condition number. The performance of the method has been demonstrated for a large number of the nodes and on uniform and non-uniform node arrangements Research Limitations: The method can at the present cope with linear thermoelasticity. Other, more complicated material behavior (viscoplasticity for example), will be tackled in one of our future publications.
COBISS.SI-ID: 3976187
The purpose of the paper is to extend and explore the application of a novel meshless Local Radial Basis Function Collocation Method (LRBFCM) in solution of a steady, laminar, natural convection flow, influenced by magnetic field. The problem is defined by coupled mass, momentum, energy and induction equations that are solved in two dimensions by using local collocation with multiquadrics radial basis functions on an overlapping five nodded sub-domains and explicit time-stepping. The fractional step method is used to couple the pressure and velocity fields. The considered problem is calculated in a square cavity with two insulated horizontal and two differentially heated vertical walls with magnetic field applied in the horizontal direction. Numerical predictions are calculated for different Grashof numbers, ranging from 10**4 to 10**6, and Hartman numbers, ranging from 0 to 100, at Prandtl numbers 0.71 and 0.14. The results of the method are compared to predictions, obtained by other numerical methods, including FLUENT code. Good agreement has been achieved. The LRBFCM has been used in this kind of problems for the first time. The main advantage of the method is its simple numerical implementation and no need for polygonisation (mesh).
COBISS.SI-ID: 2827003
An efficient numerical method based on uniform Haar wavelets is proposed for the numerical solution of second-order boundary-value problems (BVPs) arising in the mathematical modelling of deformation of beams and plates, deflection theory, deflection of a cantilever beam under a concentrated load, obstacle problems and many other engineering applications. The Haar wavelet basis permits to enlarge the class of functions used so far in the collocation framework. The performance of the Haar wavelets is compared with the Walsh wavelets, semi-orthogonal Bspline wavelets, spline functions, Adomian decomposition method (ADM), finite difference method, and Runge-Kutta method coupled with nonlinear shooting method. A more accurate solution can be obtained by wavelet decomposition in the form of a multi-resolution analysis of the function which represents the solution of a given problem. Through this analysis the solution is found on the coarse grid points, and then refined towards higher accuracy by increasing the level of the Haar wavelets. Neumann's boundary conditions which are problematic for most of the numerical methods are automatically coped with. The main advantage of the Haar wavelet based method is its efficiency and simple applicability for a variety of boundary conditions. The convergence analysis of the proposed method alongside numerical procedure for multi-point boundary value problems are given to test wider applicability and accuracy of the method.
COBISS.SI-ID: 2203899