The simulation of macrosegregation as a consequence of solidification of a binary Al4.5% Cu alloy in a 2 dimensional rectangular enclosure is tackled in the present paper. Coupled volume averaged governing equations for mass, energy, momentum and species transfer are considered. The phase properties are resolved from the Lever solidification rule, the mushy zone is modeled by the Darcy law and the liquid phase is assumed to behave like an incompressible Newtonian fluid. Double diffusive effects in the melt are modeled by the thermal and solutal Boussinesq hypothesis. The physical model is solved by the novel Local Radial Basis Function Collocation Method (LRBFCM). The involved physical relevant fields are represented on overlapping 5 noded subdomains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBFs. The fields are solved through explicit time stepping. The pressure-velocity coupling is calculated through a local pressure correction scheme. The evolution of the solidification process is presented through temperature, velocity, liquid fraction and species concentration histories in four sampling points. The fully solidified state is analyzed through final macrosegregation map in three vertical and three horizontal crosssections. The results are compared with the classical Finite Volume Method (FVM). A surprisingly good agreement of the numerical solution of both methods is shown and therefore the results can be used as a reference for future verification studies. The advantages of the represented meshless approach are its simplicity, accuracy, similar coding in 2D and 3D, and straightforward applicability in nonuniform node arrangements. The paper probably for the first time shows an application of a meshless method in such a highly nonlinear and multiphysics problem. Comment: the paper was selected to demonstrate achievements in the field of multiscale macrosegregation modelling.
COBISS.SI-ID: 1905659
We describe the original development of meshless methods for calculation of diffusion problems on extremely non-uniform distribution of nodes, used in large gradient situations. A least squares method is used instead of collocation in such situations. The described research and experiences gained have been incorporated in multiscale (micro/macro) simulation systems for casting, rolling and heat treatment. Comment: the paper was selected as typical in the field of microstructure modelling.
COBISS.SI-ID: 1998331
This paper introduces an effective H-adaptive upgrade to solution of the transport phenomena by the novel Local Radial Basis Function Collocation Method (LRBFCM). The transport variable is represented on overlapping 5-noded influence-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the variable are calculated from the respective derivatives of the RBFs. The transport equation is solved through explicit time stepping. The H-adaptive upgrade includes refinement/derefinement of one to four nodes to/from the vicinity of the reference node. The number of the nodes added or removed depends on the topology of the reference node vicinity. The refinement/derefinement is triggered by an error indicator, which very simply depends on the ratio between the norm of the collocation coefficients and collocation matrix. The refinement/derefinement is proportional with the growth/decay of this indicator. Such adaptivity much increases the accuracy/performance ratio of the method. The performance of the method is numerically tested on two-dimensional Burger’s equation. The results are compared with different numerical solutions, published in literature. Outstanding CPU efficiency and accuracy are clearly demonstrated from the results. The paper probably for the first time shows such a simple and effective H-adaptive meshless method, designed on five noded influence domain. The advantages of the represented meshless approach are its simplicity, accuracy, similar coding in 2D and 3D, straightforward applicability in non-uniform node arrangements, and native parallel implementation. Comment: the paper was selected to demonstrate achievements in the field of adaptivity.
COBISS.SI-ID: 2177275
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). Comment: the paper was selected for demonstration of achievements in the field of multiphysics simulations with meshless methods.
COBISS.SI-ID: 2827003
In evolutionary multiobjective optimization it is very important to be able to visualize approximations of the Pareto front (called approximation sets) found by multiobjective evolutionary algorithms. While scatter plots can be used for visualizing 2D and 3D approximation sets, more advanced approaches are needed to handle four or more objectives. This paper presents a comprehensive review of the existing visualization methods used in evolutionary multiobjective optimization, showing their outcomes on two novel 4D benchmark approximation sets. In addition, a visualization method that uses prosection (projection of a section) to visualize 4D approximation sets is proposed. The method reproduces the shape, range and distribution of vectors in the observed approximation sets well and can handle multiple large approximation sets while being robust and computationally inexpensive. Even more importantly, for some vectors, the visualization with prosections preserves the Pareto dominance relation and relative closeness to reference points. The method is analyzed theoretically and demonstrated on several approximation sets. Comment: the paper was selected for demonstration of achievements in the field of multiobjective optimisation.
COBISS.SI-ID: 27961383