Solidification modelling with a control volume method on domains subjected to viscoplastic deformation

Davey, Keith; Rodriguez, N. J.

doi:10.1016/s0307-904x(01)00045-2

Cited by 3 publications

(7 citation statements)

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“…important contribution. The work extends the ideas developed in references [28,29], which are restricted to capacitance formulations for phase-change problems described via transport equations. The approach adopted here is founded on transport equations for an arbitrary control volume (CV) moving relative to the transporting material.…”

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confidence: 85%

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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confidence: 85%

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

Davey

Mondragon

2010

Numerical Meth Engineering

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“…refer to a material reference system, a spatial reference system and a computational reference system coordinate respectively. The relations between the material derivative and an arbitrary Lagrangian-Eulerian derivative with respect to the spatial derivative are defined by the following expressions [1][2][3][4][5][6][7];…”

Section: -Transport Equation In Elastoplastic Control Volumementioning

confidence: 99%

“…Using the Reynolds and Divergence transport theorem at the same time in the absence of discontinuity, above-mentioned integral equation becomes a differential form below [1][2][3][4][5][6][7] (37) ̂ ̂ ( ) ( )…”

Section: -Equivalent Nonphysical Variable Equationsmentioning

confidence: 99%

“…Davey used the transport equations in the field of modeling heat transfer in the presence and absence of boundary and material discontinuities [1][2][3][4][5][6][7]. The performance of the capacity control methods for convection-solidification problems was investigated by Davey [1].…”

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confidence: 99%

“…The performance of the capacity control methods for convection-solidification problems was investigated by Davey [1]. In this investigation, the convective heat transfer applied to a semi-infinite domain without solidification, isothermal solidification was applied to a semi-infinite domain with and without convection, solidification of a deforming cube; mushy solidification and extrusion of a solidifying body; mushy solidfication were tested.…”

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confidence: 99%

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