Simulation of a macrosegregation benchmark with a meshless diffuse approximate method

Simulation of a macrosegregation benchmark with a meshless diffuse approximate method PurposeThe purpose of this paper is to simulate a macrosegregation solidification benchmark by a meshless diffuse approximate method. The benchmark represents solidification of Al 4.5 wt per cent Cu alloy in a 2D rectangular cavity, cooled at vertical boundaries.Design/methodology/approachA coupled set of mass, momentum, energy and species equations for columnar solidification is considered. The phase fractions are determined from the lever solidification rule. The meshless diffuse approximate method is structured by weighted least squares method with the second-order monomials for trial functions and Gaussian weight functions. The spatial localization is made by overlapping 13-point subdomains. The time-stepping is performed in an explicit way. The pressure-velocity coupling is performed by the fractional step method. The convection stability is achieved by upstream displacement of the weight function and the evaluation point of the convective operators.FindingsThe results show a very good agreement with the classical finite volume method and the meshless local radial basis function collocation method. The simulations are performed on uniform and non-uniform node arrangements and it is shown that the effect of non-uniformity of the node distribution on the final segregation pattern is almost negligible.Originality/valueThe application of the meshless diffuse approximate method to simulation of macrosegregation is performed for the first time. An adaptive upwind scheme is successfully applied to the diffuse approximate method for the first time. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

Simulation of a macrosegregation benchmark with a meshless diffuse approximate method

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Publisher
Emerald Group Publishing Limited
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0961-5539
D.O.I.
10.1108/HFF-04-2017-0143
Publisher site
See Article on Publisher Site

Abstract

PurposeThe purpose of this paper is to simulate a macrosegregation solidification benchmark by a meshless diffuse approximate method. The benchmark represents solidification of Al 4.5 wt per cent Cu alloy in a 2D rectangular cavity, cooled at vertical boundaries.Design/methodology/approachA coupled set of mass, momentum, energy and species equations for columnar solidification is considered. The phase fractions are determined from the lever solidification rule. The meshless diffuse approximate method is structured by weighted least squares method with the second-order monomials for trial functions and Gaussian weight functions. The spatial localization is made by overlapping 13-point subdomains. The time-stepping is performed in an explicit way. The pressure-velocity coupling is performed by the fractional step method. The convection stability is achieved by upstream displacement of the weight function and the evaluation point of the convective operators.FindingsThe results show a very good agreement with the classical finite volume method and the meshless local radial basis function collocation method. The simulations are performed on uniform and non-uniform node arrangements and it is shown that the effect of non-uniformity of the node distribution on the final segregation pattern is almost negligible.Originality/valueThe application of the meshless diffuse approximate method to simulation of macrosegregation is performed for the first time. An adaptive upwind scheme is successfully applied to the diffuse approximate method for the first time.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Feb 5, 2018

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