Control of the freezing interface motion in two‐dimensional solidification processes using the adjoint method

Shinill Kang, Nicholas Zabaras

Research output: Contribution to journalArticle

40 Citations (Scopus)

Abstract

The aim of this work is to calculate the optimum history of boundary cooling conditions that, in two‐dimensional conduction driven solidification processes, results in a desired history of the freezing interface location/motion. The freezing front velocity and heat flux on the solid side of the front, define the obtained solidification microstructure that can be selected such that desired macroscopic mechanical properties and soundness of the final cast product are achieved. The so‐called two‐dimensional inverse Stefan design problem is formulated as an infinite‐dimensional minimization problem. The adjoint method is developed in conjunction with the conjugate gradient method for the solution of this minimization problem. The sensitivity and adjoint equations are derived in a moving domain. The gradient of the cost functional is obtained by solving the adjoint equations backward in time. The sensitivity equations are solved forward in time to compute the optimal step size for the gradient method. Two‐dimensional numerical examples are analysed to demonstrate the performance of the present method.

Original languageEnglish
Pages (from-to)63-80
Number of pages18
JournalInternational Journal for Numerical Methods in Engineering
Volume38
Issue number1
DOIs
Publication statusPublished - 1995 Jan 1

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Adjoint Method
Adjoint Equation
Freezing
Solidification
Minimization Problem
Conjugate gradient method
Gradient methods
Motion
Gradient Method
Conjugate Gradient Method
Soundness
Heat Flux
Conduction
Mechanical Properties
Cooling
Heat flux
Microstructure
Gradient
Calculate
Numerical Examples

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

Cite this

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