Numerical Computation of Critical Flow Over a Spillway by Means of Minimization of Violation of Negative Curvature Condition

Mejak, George

doi:10.1002/(sici)1097-0363(19960215)22:3<151::aid-fld333>3.0.co;2-s

Cited by 2 publications

(2 citation statements)

References 12 publications

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“…How to compute the individual terms in @J n =@h has already been described. Also, the computation of @J n =@u readily follows from (32) or (33) and thus it remains only to consider @u =@h. Evidently, referring to (20) we have…”

Section: Computation Of the Cost Functions And Their Gradientsmentioning

confidence: 99%

“…A solution to these limitations is a modiÿcation of the requisite conditions that in and out are parallel to y and x co-ordinate axes, respectively. This can be done following the idea 32 where out is allowed to move together with free . Nevertheless, from the point of numerics it is of interest to consider the problem in its original form.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Finite Element Solution of a Model Free Surface Problem by the Optimal Shape Design Approach

Mejak

1997

Int. J. Numer. Meth. Engng.

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SUMMARYOptimal shape design approach is applied to numerical computation of a model potential free boundary value problem. The problem is discretized using the ÿnite element method. To test the approach the problem is formulated in both velocity potential and stream function formulation and four di erent ÿnite element discretizations are used. Associated minimization problem is solved using the quasi-Newton method. Gradient of the cost function is computed by solving the algebraic adjoint equation. Gravity and surface tension forces are included in the model. Viability of the method is showed by solving problems with important e ects of gravity and surface tension forces. ? 1997 by John Wiley & Sons, Ltd.

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Section: Computation Of the Cost Functions And Their Gradientsmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Finite Element Solution of a Model Free Surface Problem by the Optimal Shape Design Approach

Mejak

1997

Int. J. Numer. Meth. Engng.

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Optimization of cross-section of hollow prismatic bars in torsion

Mejak

2000

Commun. Numer. Meth. Engng.

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The problem of optimal shape design of a doubly connected prismatic bar in torsion is formulated and solved numerically by the ÿnite element method. The cost function is torsional rigidity of the domain, constraint is the constant area of the cross-section while shape parameters are co-ordinates of the ÿnite element nodes along the variable boundary. The variable boundary is either the inner or outer boundary of the domain. A dual problem of minimizing the area at the constant torsional rigidity is also considered. The problem is solved directly by optimizing the cost function with respect to the shape parameters. Numerical examples are given for two benchmark problems.

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Numerical Computation of Critical Flow Over a Spillway by Means of Minimization of Violation of Negative Curvature Condition

Cited by 2 publications

References 12 publications

Finite Element Solution of a Model Free Surface Problem by the Optimal Shape Design Approach

Finite Element Solution of a Model Free Surface Problem by the Optimal Shape Design Approach

Optimization of cross-section of hollow prismatic bars in torsion

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