Sensitivity and optimization for shape and non‐linear boundary conditions in thermal boundary elements

Davey, Keith; Clark, L D

doi:10.1002/nme.577

Cited by 6 publications

(2 citation statements)

References 21 publications

(34 reference statements)

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“…where div i v + = divv + − Dv + n s , n s [32] with v + defined local to i , and where (Dv + ) m = *v + /*x m and ·, · stands for inner product. The derivative on the LHS of (20) is defined in the sense of (18).…”

Section: Discontinuities For Non-physical Equationsmentioning

confidence: 99%

A non‐physical enthalpy method for the numerical solution of isothermal solidification

Davey

Mondragon

2010

Numerical Meth Engineering

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SUMMARYIn this paper, a new formulation for the solution of the discontinuous isothermal solidification problem is presented. The formulation has similarities with the now classical capacitance and source methods traditionally used in commercial software. However, the new approach focuses on the solution of the governing enthalpy-transport equation rather than the governing parabolic partial differential heat equation. The advantage is that discontinuous physics can be accounted for without approximation and the arbitrariness common to classic approaches is avoided. Also introduced is the concept of non-physical enthalpy, which unlike physical enthalpy has numerical values that are not moving-frame invariant. Understanding the behaviour of the non-physical enthalpy is central to the successful treatment of discontinuities. A particular drawback is that non-physical enthalpy is non-intuitive and new mathematical constructs are required to describe its behaviour. This involves the introduction of transport equations, which provide the new concept of relative moving-frame invariance for the non-physical enthalpy. The principal advantage, however, is that a unified methodology is established for the treatment of discontinuities. This is shown to establish real rigour and in many respects the formulation highlights the erroneous choices made with established classical approaches and casts in a totally new light a somewhat traditional problem. The new methodology is applied to a range of simple problems not only to provide an in-depth treatment and for ease of understanding but also to best describe the behaviour of the non-intuitive non-physical enthalpy. Demonstrated in the paper is the methods' remarkable accuracy and stability.

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Section: Discontinuities For Non-physical Equationsmentioning

confidence: 99%

A non‐physical enthalpy method for the numerical solution of isothermal solidification

Davey

Mondragon

2010

Numerical Meth Engineering

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“…where © is twice the mean curvature of the boundary, v is the deformation rate and n is the unit outward normal. If the adjoint variable satis®es equation (33), then the terms @T =@b p and @ ¶=@b p are eliminated from the design sensitivity DI =Db p [23]. If this is applied in equation ( 28) after using Green's ®rst theorem on the domain integral and identities ( 35) and (36) are applied, then…”

Section: Sensitivity Analysismentioning

confidence: 99%

Optimization for boiling heat transfer determination and enhancement in pressure die casting

Davey

Hinduja

Clark

2002

Proceedings of the Institution of Mechanical Engineers, Part B:

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Boiling in cooling channels has recently been demonstrated to be an effective mechanism for heat extraction in pressure die casting. Boiling heat transfer can be enhanced by cooling channel shape optimization. The occurrence of boiling presents a non-linear thermal problem which, when combined with shape optimization, necessitates the solving of non-linear equations for each channel configuration. In this paper a methodology is presented that involves the use of optimization for the combined determination of channel shapes and heat transfer coefficients. It is shown in the paper how this approach results in the accurate determination of boiling heat transfer coefficients on the final optimized cooling channel configuration. The non-linear thermal problem is calculated at very little computational cost over that required for a comparable linear problem. Focus in the paper is on the application of the methodology to the pressure die casting process. The approach adopted is founded on a design sensitivity analysis using the material derivative adjoint variable method. The thermal model for the pressure die casting process is founded on the boundary element method and the optimization is performed using a conjugate gradient scheme. Geometrical constraints are enforced using buffer elements superimposed on to the boundary element mesh. Numerical and experimental trials are performed to demonstrate the potential of the new optimization methodology.

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Weak discontinuity annihilation in solidification modelling

Mondragon¹,

Davey²

2011

Computers & Structures

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Sensitivity and optimization for shape and non‐linear boundary conditions in thermal boundary elements

Cited by 6 publications

References 21 publications

A non‐physical enthalpy method for the numerical solution of isothermal solidification

A non‐physical enthalpy method for the numerical solution of isothermal solidification

Optimization for boiling heat transfer determination and enhancement in pressure die casting

Weak discontinuity annihilation in solidification modelling

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