Cheng Deng^1,2, Hui Zheng^2,*, Liangyong Gong¹, Rongping Zhang¹, Mengqi Wang³

CMES-Computer Modeling in Engineering & Sciences, Vol.142, No.2, pp. 2147-2172, 2025, DOI:10.32604/cmes.2025.059750 - 27 January 2025

Abstract Since the plasticity of soil and the irregular shape of the excavation, the efficiency and stability of the traditional local radial basis function (RBF) collocation method (LRBFCM) are inadequate for analyzing three-dimensional (3D) deformation of deep excavation. In this work, the technique known as the direct method, where the local influence nodes are collocated on a straight line, is introduced to optimize the LRBFCM. The direct method can improve the accuracy of the partial derivative, reduce the size effect caused by the large length-width ratio, and weaken the influence of the shape parameters on the More >

U. Hanoglu¹, B. Šarler^1,2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.5, pp. 447-479, 2015, DOI:10.3970/cmes.2015.109.447

Abstract The aim of this paper is to demonstrate the use of the novel Local Radial Basis Function Collocation Method (LRBFCM) [Šarler and Vertnik (2006)] in an industrial coupled thermo-mechanical problem of hot shape rolling of steel. The physical concept of such a large deformation problem is based on a two dimensional traveling slice model [Glowacki (2005)], which assumes deformation and heat flow only in the perpendicular direction to rolling. The solution is performed based on strong formulation. Elliptic Node Generation (ENG) is applied to reposition the nodes over a slice when necessary in order to… More >

K. Mramor¹, R. Vertnik^2,3, B. Šarler^1,3,4,5

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.4, pp. 327-352, 2013, DOI:10.3970/cmes.2013.092.327

Abstract The purpose of the present 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 subdomains 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… More >

K. Mramor¹, R. Vertnik^2,3, B. Šarler^1,3,4,5

CMC-Computers, Materials & Continua, Vol.36, No.1, pp. 1-21, 2013, DOI:10.3970/cmc.2013.036.001

Abstract This paper explores the application of Local Radial Basis Function Collocation Method (LRBFCM) [Šarler and Vertnik (2006)] for solution of Newtonian incompressible 2D fluid flow for a lid driven cavity problem [Ghia, Ghia, and Shin (1982)] in primitive variables. The involved velocity and pressure fields are represented on overlapping five-noded sub-domains through collocation by using Radial Basis Functions (RBF). The required first and second derivatives of the fields are calculated from the respective derivatives of the RBF’s. The momentum equation is solved through explicit time stepping. The method is alternatively structured with multiquadrics and inverse… More >

Gregor Kosec¹, Miha Založnik², Božidar Šarler¹, Hervé Combeau²

CMC-Computers, Materials & Continua, Vol.22, No.2, pp. 169-196, 2011, DOI:10.3970/cmc.2011.022.169

Abstract The simulation of macrosegregation as a consequence of solidification of a binary Al-4.5%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… More >

G. Kosec¹, B. Šarler²

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.2, pp. 191-216, 2009, DOI:10.3970/cmes.2009.047.191

Abstract This paper explores an application of a novel mesh-free Local Radial Basis Function Collocation Method (LRBFCM) [Sarler and Vertnik (2006)] in solution of coupled heat transfer and fluid flow problems with solid-liquid phase change. The melting/freezing of a pure substance is solved in primitive variables on a fixed grid with convection suppression, proportional to the amount of the solid fraction. The involved temperature, velocity and pressure fields are represented on overlapping sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective… More >

G. Kosec¹, B. Šarler¹

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.3, pp. 197-208, 2008, DOI:10.3970/cmes.2008.025.197

Abstract This paper explores the application of the mesh-free Local Radial Basis Function Collocation Method (LRBFCM) in solution of coupled heat transfer and fluid flow problems in Darcy porous media. The involved temperature, velocity and pressure fields are represented on overlapping sub-domains 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 RBF's. The energy and momentum equations are solved through explicit time stepping. The pressure-velocity coupling is calculated iteratively, with pressure correction, predicted from the local continuity equation violation.… More >

B. Šarler¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 185-194, 2005, DOI:10.3970/cmes.2005.007.185

Abstract This paper explores the application of the mesh-free radial basis function collocation method for solution of heat transfer and fluid flow problems. The solution procedure is represented for a Poisson reformulated general transport equation in terms of a-symmetric, symmetric and modified (double consideration of the boundary nodes) collocation approaches. In continuation, specifics of a primitive variable solution procedure for the coupled mass, momentum, and energy transport representing the natural convection in an incompressible Newtonian Bussinesq fluid are elaborated. A comparison of different collocation strategies is performed based on the two dimensional De Vahl Davis steady More >