Gregor Kosec

Solution of thermo‐fluid problems by collocation with local pressure correction

Purpose – The purpose of this paper is to explore the application of the mesh‐free local radial basis function collocation method (RBFCM) in solution of coupled heat transfer and fluid‐flow problems.Design/methodology/approach – The involved temperature, velocity and pressure fields are represented on overlapping five nodded 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 RBFs. The energy and momentum equations are solved through explicit time stepping.Findings – The performance of the method is assessed on the classical two dimensional de Vahl Davis steady natural convection benchmark for Rayleigh numbers from 103 to 108 and Prandtl number 0.71. The results show good agreement with other methods at a given range.Originality/value – The pressure‐velocity coupling is calculated iteratively, with pressure correction, predicted from the local mass continuity equat...

On the Convergence of Stresses in Fretting Fatigue

Fretting is a phenomenon that occurs at the contacts of surfaces that are subjected to oscillatory relative movement of small amplitudes. Depending on service conditions, fretting may significantly reduce the service life of a component due to fretting fatigue. In this regard, the analysis of stresses at contact is of great importance for predicting the lifetime of components. However, due to the complexity of the fretting phenomenon, analytical solutions are available for very selective situations and finite element (FE) analysis has become an attractive tool to evaluate stresses and to study fretting problems. Recent laboratory studies in fretting fatigue suggested the presence of stress singularities in the stick-slip zone. In this paper, we constructed finite element models, with different element sizes, in order to verify the existence of stress singularity under fretting conditions. Based on our results, we did not find any singularity for the considered loading conditions and coefficients of friction. Since no singularity was found, the present paper also provides some comments regarding the convergence rate. Our analyses showed that the convergence rate in stress components depends on coefficient of friction, implying that this rate also depends on the loading condition. It was also observed that errors can be relatively high for cases with a high coefficient of friction, suggesting the importance of mesh refinement in these situations. Although the accuracy of the FE analysis is very important for satisfactory predictions, most of the studies in the literature rarely provide information regarding the level of error in simulations. Thus, some recommendations of mesh sizes for those who wish to perform FE analysis of fretting problems are provided for different levels of accuracy.

A Meshless Approach in Solution of Multiscale Solidification Modeling

This paper describes an overview of a new meshless solution procedure for calculation of one-domain coupled macroscopic heat, mass, momentum and species transfer problems as well as phase-field concepts of grain evolution. The solution procedure is defined on the macro [1] as well as on the micro levels [2] by a set of nodes which can be non-uniformly distributed. The domain and boundary of interest are divided into overlapping influence areas. On each of them, the fields are represented by the multiquadrics radial basis functions (RBF) collocation on a related sub-set of nodes. The time-stepping is performed in an explicit way. All governing equations are solved in their strong form, i.e. no integrations are performed. The polygonisation is not present and the formulation of the method is practically independent of the problem dimension. The solution can be easily and efficiently adapted in node redistribution and/or refinement sense, which is of utmost importance when coping with fields exhibiting sharp gradients. The concept and the results of the multiscale solidification modeling with the new approach are compared with the classical mesh-based [3] approach. The method turns out to be extremely simple to code and accurate, inclusion of the complicated physics can easily be looked over. The coding in 2D or 3D is almost identical.

Convection driven melting of anisotropic metals

Abstract This paper numerically explores melting of a pure substance with the thermal conductivity of the solid phase, assumed to be anisotropic. A two-phase test case for such situations is deduced from the standard one-phase Gobin–Le Quéré melting benchmark. The solution is presented for Prandtl number 0·02, Stefan number 0·01 and Rayleigh number 2·5 × 104 which are specific for metals. Three cases are compared in terms of the terminal interface boundary position and average liquid fraction as a function of time for isotropic case and two distinctly oriented principal directions of the thermal conductivity tensor. The calculations have been performed by using the one-domain enthalpy formulation with artificial melting interval and the recently developed explicit local radial basis function collocation method (LRBFCM) which belongs to the entirely new generation of meshless methods. The results are not sensitive to the increased thermal conductivity of the solid phase in the direction parallel with the heated boundary but sensitive with the increase of the thermal conductivity of the solid phase in the direction perpendicular to the heated boundary.

Parallel Scientific Computing

The background and motivation for the development of solution methodologies for partial differential equations are given with an overview of the related work and the relevant publications.

Detection of heart rate variability from a wearable differential ECG device

The precise heart rate variability is extracted from an ECG signal measured by a wearable sensor that constantly records the heart activity of an active subject for several days. Due to the limited resources of the wearable ECG device the signal can only be sampled at relatively low, approximately 120 Hz, frequency. Besides low sampling rate the signal from a wearable sensor is also burdened with much more noise than the standard 12-channel ambulatory ECG, mostly due to the design of the device, i.e. the electrodes are positioned relatively close to each other, and the fact that the subject is active during the measurements. To extract heart rate variability with 1 ms precision, i.e. 10 times more accurate than the sample rate of the measured signal, a two-step algorithm is proposed. In first step an approximate global search is performed, roughly determining the point of interest, followed by a local search based on the Moving Least Squares approximation to refine the result. The methodology is evaluated in terms of accuracy, noise sensitivity, and computational complexity. All tests are performed on simulated as well as measured data. It is demonstrated that the proposed algorithm provides accurate results at a low computational cost and it is robust enough for practical application.

Cellular Automata Supporting -Connectivity

We propose a new algorithm based on cellular automation (CA) for preserving -connectivity, . The CA algorithm transforms an initial grid configuration in a grid with same number of holes but without 1-connected components. Also, maximal thinning of -connected components, , is achieved. The grid can be used as initial for investigating properties of initial grid. Computational performances are evaluated and measured on real cases. The obtained results indicate that the proposed approach achieves comparable complexity as standard approaches; however, the speed-up and scalability of the proposed algorithm are not limited by the number of processing nodes.

Adaptive meshfree method for thermo-fluid problems with phase change

In the present paper, the recently developed local meshfree method solution of thermo-fluid problems is modified from the collocation to the combined collocation and weighted least squares approach and upgraded with an h-adaptive strategy. A one domain enthalpy formulation is used for modelling the solid-liquid energy transport and the liquid phase is assumed to behave as an incompressible Newtonian fluid modelled by the Boussinesq hypothesis. The involved temperature, enthalpy, velocity and pressure fields are represented on overlapping local sub-domains through weighted least squares approximation (by a truncated Gaussian weight in the domain nodes) and collocation (at the boundary nodes) by using multiquadrics Radial Basis Functions (RBF). The transport equations are solved through explicit time stepping. The pressure-velocity coupling is calculated iteratively through a novel local pressure correction algorithm. The node adaptivity is established through a phase-indicator and a node refinement strategy that takes into account the dynamic number of neighbouring nodes. The proposed approach is used to solve the standard Gobin Le Quere melting benchmark with tin at Stefan number (Ste) 0.01, Prandtl number (Pr) 0.02, and Rayleigh number (Ra) 2.5e4. The node distribution changes through the simulation as the melting front advances. The solid is consequently computed at much lower node distribution density in comparison with the liquid, which speeds up the simulation and at the same time preserves accuracy. The latter issue has been demonstrated by comparison with the results of other combinations of numerical methods and formulations that attempted this benchmark in the past.

An improved radial basis-pseudospectral method with hybrid Gaussian-cubic kernels

Abstract While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic conditioning (1) in their most accurate flat basis function regime, and (2) when problem sizes are scaled up to become of practical interest. The present study considers a strategy to improve on these two issues by means of using hybrid radial basis functions that combine cubic splines with Gaussian kernels. The parameters, controlling Gaussian and cubic kernels in the hybrid RBF, are selected using global particle swarm optimization. The proposed approach has been tested with radial basis-pseudospectral method for numerical approximation of Poisson, Helmholtz, and Transport equation. It was observed that the proposed approach significantly reduces the ill-conditioning problem in the RBF-PS method, at the same time, it preserves the stability and accuracy for very small shape parameters. The eigenvalue spectra of the coefficient matrices in the improved algorithm were found to be stable even at large degrees of freedom, which mimic those obtained in pseudospectral approach. Also, numerical experiments suggest that the hybrid kernel performs significantly better than both pure Gaussian and pure cubic kernels.

Numerical Solution of Natural Convection Problems by a Meshless Method

Natural convection is a phenomenon where fluid motion is generated by density changes due to the temperature or concentration variations in a gravity field. The computational modelling of systems with natural convection (Bejan, 2004) has become a highly popular research subject due to its pronounced influence in better understanding of nature as well as in the development of the advanced technologies. Melting of the polar ice caps, the global oceans dynamics, various weather systems, water transport, soil erosion and denudation, magma transport and manufacturing of nano-materials, improving casting processes, energetic studies, exploitation of natural resources, welding, casting and advanced solidifications are two typical contemporary example groups where natural convection plays an important role. This chapter deals with the numerical approach towards solution of this type of problems by a meshless technique. The main part of the solution procedure is focused on the general transport equation treatment and the pressure velocity coupling strategy. The transport phenomena are solved by a local meshless method and explicit time stepping. The local variant of Radial Basis Function Collocation Method (LRBFCM) has been previously developed for diffusion problems (Sarler and Vertnik, 2006), convection-diffusion solid-liquid phase change problems (Vertnik and Sarler, 2006) and subsequently successfully applied in industrial process of direct chill casting (Vertnik, et al., 2006). The fluid flow, which is generally a global problem, is treated by the proposed local iterative method. Instead of solving the pressure Poisson equation or/and pressure correction Poisson equation (Divo and Kassab, 2007) a more simplified local pressure-velocity coupling (LPVC) (Kosec and Sarler, 2008a) algorithm is proposed where the pressure-correction is predicted from the local mass continuity violation similar to the SOLA algorithm (Hong, 2004). The presented solution procedure represents a variant of already developed global approach (Sarler, et al., 2004a, Sarler, 2005). In this chapter, such a local solution procedure is tested with the standard free fluid flow benchmark test (de Vahl Davis natural convection test (de Vahl Davis, 1983)). The test is especially convenient for benchmarking purposes as there are several numerical solutions published in the literature (Divo and Kassab, 2007, Hortmann, et al., 1990, Manzari, 1999, Prax, et al., 1996, Sadat and Couturier, 2000, Sarler, 2005, Wan, et al., 2001).