Volume 48, Number 1, January-February 2014
|Page(s)||87 - 106|
|Published online||15 November 2013|
A Bermúdez–Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes
1 Department of Applied Mathematics. Universidade de Santiago
de Compostela, 15782 Santiago de Compostela, Spain. ;
2 Centro Universitario de la Defensa Zaragoza, Academia General Militar, Ctra. Huesca, s/n, 50090 Zaragoza, Spain.
Revised: 22 May 2013
The aim of this work is to present a computationally efficient algorithm to simulate the deformations suffered by a viscoplastic body in a solidification process. This type of problems involves a nonlinearity due to the considered thermo-elastic-viscoplastic law. In our previous papers, this difficulty has been solved by means of a duality method, known as Bermúdez–Moreno algorithm, involving a multiplier which was computed with a fixed point algorithm or a Newton method. In this paper, we will improve the former algorithms by means of a generalized duality method with variable parameters and we will present numerical results showing the applicability of the resultant algorithm to solidification processes. Furthermore, we will describe a numerical procedure to choose a constant parameter for the Bermúdez–Moreno algorithm which gives good results when it is applied to solidification processes.
Mathematics Subject Classification: 74C10 / 74D10 / 65N30
Key words: Viscoplastic materials / duality methods / solidification process
© EDP Sciences, SMAI 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.