Adaptive Mesh Refinement of the Solidification Front in Continuous Caster Simulations

Author(s):  
Xiang Zhou ◽  
Matthew T. Moore ◽  
Haibo Ma ◽  
Armin K. Silaen ◽  
Chenn Q. Zhou

Abstract A better understanding of the complex phenomena that occur along the solidification front in a continuous casting process is a fundamental necessity for reliably evaluating whether specific casting conditions inherently influence defect generation rates. Due to the intrinsic nature of the casting process, engineers are restricted in their ability to obtain accurate measurements of the shell development during casting operations. Through the end of the 20th century and up to the present, significant progress has been made in overcoming these limitations through the development of numerical models capable of accurately replicating the behavior of targeted phenomena that occur during the casting process. Continual revisions to these models have produced notable results; however, these approaches have primarily implemented predefined mesh representations of a system for simulation. The mesh utilized in any numerical simulation directly influences the results the model can generate. Developing an appropriate mesh capable of replicating the complex behavior of a system can require significant consideration of various factors involved in the construction of the mesh, the physics of the process being modeled, along with the solvers utilized in evaluating the system. Inadequate mesh construction may yield insufficient refinement for capturing desired aspects of a system or generating large areas of unneeded refinement. This article discusses characteristic behaviors and limitations of a select grouping of meshing algorithms currently available, as well as potential methods for avoiding mesh-driven solutions when simulating the solidification process in a continuous caster. Particular emphasis is placed on incorporating adaptive mesh refinement to lessen the potential for mesh-driven solutions and to reduce unnecessarily high cell-counts of the mesh through the restructuring of the mesh in accordance with the active simulation results. A numerical model was developed using the Simcenter™ STAR-CCM+™ software, and using Eulerian multiphase VOF melting and solidification models for steady-state simulations. Casting conditions and measurement data (provided by an industrial collaborator) were employed in defining boundary conditions, as well as for the model validation. The predicted shell profiles demonstrated good agreement with shell-thickness measurements obtained from the quarter-mold location of a recovered break-out shell segment.

2021 ◽  
pp. 1-19
Author(s):  
Sergej Konstantinovich Grigorjev ◽  
Anton Alekseevich Bay ◽  
Dmitri Sergeevich Boykov ◽  
Gennadiy Alekseevich Bagdasarov ◽  
Yulia Sergeevna Sharova

Adaptive Mesh Refinement (AMR) is widely used today as a way to solve problems in the mechanics of continuous media, which makes it possible to increase the accuracy of the solution at an economical cost of computational resources. The paper presents new structures for storing and processing data for octree mesh adaptation in the leaf model paradigm. The current version of the technique implements a set of algorithms focused on applications to cluster-type parallel computing systems: dynamic mesh adaptation, data structure synchronization, and load balancing of the computing complex. The developed toolkit supports the functionality required for the implementation of various numerical models of continuum mechanics. As an example of possible applications, a difference schemes for heat conduction and gas dynamics using the developed AMR technique are discussed. The results of numerical experiments with model problems are presented.


2018 ◽  
Vol 50 (04) ◽  
pp. 561-570
Author(s):  
I. A. QAZI ◽  
A. F. ABBASI ◽  
M. S. JAMALI ◽  
INTIZAR INTIZAR ◽  
A. TUNIO ◽  
...  

Author(s):  
Alexander Haberl ◽  
Dirk Praetorius ◽  
Stefan Schimanko ◽  
Martin Vohralík

AbstractWe consider a second-order elliptic boundary value problem with strongly monotone and Lipschitz-continuous nonlinearity. We design and study its adaptive numerical approximation interconnecting a finite element discretization, the Banach–Picard linearization, and a contractive linear algebraic solver. In particular, we identify stopping criteria for the algebraic solver that on the one hand do not request an overly tight tolerance but on the other hand are sufficient for the inexact (perturbed) Banach–Picard linearization to remain contractive. Similarly, we identify suitable stopping criteria for the Banach–Picard iteration that leave an amount of linearization error that is not harmful for the residual a posteriori error estimate to steer reliably the adaptive mesh-refinement. For the resulting algorithm, we prove a contraction of the (doubly) inexact iterates after some amount of steps of mesh-refinement/linearization/algebraic solver, leading to its linear convergence. Moreover, for usual mesh-refinement rules, we also prove that the overall error decays at the optimal rate with respect to the number of elements (degrees of freedom) added with respect to the initial mesh. Finally, we prove that our fully adaptive algorithm drives the overall error down with the same optimal rate also with respect to the overall algorithmic cost expressed as the cumulated sum of the number of mesh elements over all mesh-refinement, linearization, and algebraic solver steps. Numerical experiments support these theoretical findings and illustrate the optimal overall algorithmic cost of the fully adaptive algorithm on several test cases.


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