Design of Two-Dimensional Stefan Processes With Desired Freezing Front Motions

Zabaras, Nicholas; Ruan, Yimin; Richmond, O.

doi:10.1080/10407799208944907

Cited by 57 publications

(28 citation statements)

References 10 publications

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“…The author presents several numerical examples. Zabaras and coworkers [29] discuss a design problem for two-dimensional Stefan problems. Their approach is based on a deforming finite element formulation.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of the Classical Two-Phase Stefan Problem in Level Set Formulation

Bernauer¹,

Herzog²

2011

SIAM J. Sci. Comput.

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Optimal control (motion planning) of the free interface in classical two-phase Stefan problems is considered. The evolution of the free interface is modeled by a level set function. The first-order optimality system is derived on a formal basis. It provides gradient information based on the adjoint temperature and adjoint level set function.Suitable discretization schemes for the forward and adjoint systems are described. Numerical examples verify the correctness and flexibility of the proposed scheme.

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Section: Introductionmentioning

confidence: 99%

Optimal Control of the Classical Two-Phase Stefan Problem in Level Set Formulation

Bernauer¹,

Herzog²

2011

SIAM J. Sci. Comput.

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“…The coefficients of this combination are determined by the least square method for the boundary of a domain. In papers [9][10][11], authors used dynamic programming or minimization techniques in *Author to whom all correspondence should be addressed. The authors wish to thank the reviewers for their valuable criticisms and suggestions, leading to the present improved version of our paper, finite-and infinite-dimensional space.…”

Section: Introductionmentioning

confidence: 99%

One-phase inverse stefan problem solved by adomian decomposition method

Grzymkowski

Sota

2006

Computers & Mathematics with Applications

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“…Some research attention has also been directed towards inverse convection and uid ow control problems due to their practical relevance [9; 10]. Over the years, the developed methodologies have been simultaneously extended to solidiÿcation process design [11][12][13][14][15][16][17][18][19]. The main emphasis of the above papers has been the design of mold heating=cooling conditions in order to achieve a solid-liquid interface growth with a desired interfacial ux G and front velocity C f .…”

Section: Introductionmentioning

confidence: 99%

Inverse design of directional solidification processes in the presence of a strong external magnetic field

Sampath

Zabaras

2001

Numerical Meth Engineering

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SUMMARYA computational method for the design of directional alloy solidiÿcation processes is addressed such that a desired growth velocity v f under stable growth conditions is achieved. An externally imposed magnetic ÿeld is introduced to facilitate the design process and to reduce macrosegregation by the damping of melt ow. The design problem is posed as a functional optimization problem. The unknowns of the design problem are the thermal boundary conditions. The cost functional is taken as the square of the L 2 norm of an expression representing the deviation of the freezing interface thermal conditions from the conditions corresponding to local thermodynamic equilibrium. The adjoint method for the inverse design of continuum processes is adopted in this work. A continuum adjoint system is derived to calculate the adjoint temperature, concentration, velocity and electric potential ÿelds such that the gradient of the L 2 cost functional can be expressed analytically. The cost functional minimization process is realized by the conjugate gradient method via the FE solutions of the continuum direct, sensitivity and adjoint problems. The developed formulation is demonstrated with an example of designing the boundary thermal uxes for the directional growth of a germanium melt with dopant impurities in the presence of an externally applied magnetic ÿeld. The design is shown to achieve a stable interface growth at a prescribed desired growth rate.

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Design of Two-Dimensional Stefan Processes With Desired Freezing Front Motions

Cited by 57 publications

References 10 publications

Optimal Control of the Classical Two-Phase Stefan Problem in Level Set Formulation

Optimal Control of the Classical Two-Phase Stefan Problem in Level Set Formulation

One-phase inverse stefan problem solved by adomian decomposition method

Inverse design of directional solidification processes in the presence of a strong external magnetic field

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