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 language | English |
|---|---|
| Pages (from-to) | 63-80 |
| Number of pages | 18 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 38 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1995 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Engineering(all)
- Applied Mathematics
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Control of the freezing interface motion in two‐dimensional solidification processes using the adjoint method. / Kang, Shinill; Zabaras, Nicholas.
In: International Journal for Numerical Methods in Engineering, Vol. 38, No. 1, 01.01.1995, p. 63-80.Research output: Contribution to journal › Article
TY - JOUR
T1 - Control of the freezing interface motion in two‐dimensional solidification processes using the adjoint method
AU - Kang, Shinill
AU - Zabaras, Nicholas
PY - 1995/1/1
Y1 - 1995/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0028992098&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0028992098&partnerID=8YFLogxK
U2 - 10.1002/nme.1620380105
DO - 10.1002/nme.1620380105
M3 - Article
AN - SCOPUS:0028992098
VL - 38
SP - 63
EP - 80
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 1
ER -