A Taylor discontinuous Galerkin method for the thermal solution in 3D mold filling

Pichelin, Élisabeth; Coupez, Thierry

doi:10.1016/s0045-7825(99)00011-0

Cited by 30 publications

(19 citation statements)

References 8 publications

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“…-a continuous P1 + /P1 element belonging to the bubble family [1], where the bubble has been discretized by four subtetrahedra, also called the "hat-function", allowing an exact integration [49,50]. -a P1 + +/P1 element with bubble and linear discontinuous pressure [14].…”

Section: The Algebraic Systemmentioning

confidence: 99%

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Fractional Step Like Schemes for Free Surface Problems with Thermal Coupling Using the Lagrangian PFEM

2006

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The method presented in Aubry et al. (Comput Struc 83:1459-1475 for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of motion is extended to three dimensions (3D) with particular emphasis on mass conservation. A modified fractional step (FS) based on the pressure Schur complement (Turek 1999), and related to the class of algebraic splittings Quarteroni et al. (Comput Methods Appl Mech Eng 188:505-526, 2000), is used and a new advantage of the splittings of the equations compared with the classical FS is highlighted for free surface problems. The temperature is semi-coupled with the displacement, which is the main variable in a Lagrangian description. Comparisons for various mesh Reynolds numbers are performed with the classical FS, an algebraic splitting and a monolithic solution, in order to illustrate the behaviour of the Uzawa operator and the mass conservation. As the classical fractional step is equivalent to one iteration of the Uzawa algorithm performed with a standard Laplacian as a preconditioner, it will behave well only in a Reynold mesh number domain where the preconditioner is efficient. Numerical results are provided to assess the superiority of the modified algebraic splitting to the classical FS.

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Section: The Algebraic Systemmentioning

confidence: 99%

“…One common numerical problem in mould filling appears with the thermal shock between the cold mould and the boiling casting, so that wiggles constantly appear with a classical discretization. A short review of possible remedies is commented in [49]. A mixed discretization temperature/heat flux may avoid this problem.…”

Section: The Thermal Problemmentioning

confidence: 99%

Fractional Step Like Schemes for Free Surface Problems with Thermal Coupling Using the Lagrangian PFEM

2006

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“…Finally, we wish to mention that most of the numerical modeling studies in injection molding are based on the lubrication approximation to formulate the mold filling problems (see, e.g., Williams and Lord 1975;Hieber and Shen 1980;Dupret and Vanderschuren 1988;Chiang et al 1991;Dupret et al 1999), although a number of recent papers use a fully three-dimensional approach (see, e.g., Pichelin and Coupez 1999;Ilinca and He´tu 2001;Michaeli et al 2001) to address specific problems that need to solve the full Navier-Stokes equations. Nevertheless, all published theoretical studies and simulations are far from predicting flow-front finger-like instabilities described in this study due to the lack of physics in the models used.…”

Section: Remarksmentioning

confidence: 99%

Elastic flow-front fingering instability in flowing polymer solutions

2005

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“…In that case, standard Galerkin methods can generate solutions polluted by spatial oscillations [8] , which are mainly due to the important temperature gradients. The solution of the thermal problem must be able to account for thermal shock occurring for instance, when a hot polymer comes into contact with a cold mold.…”

Section: Discrete Scheme For Energy Equationmentioning

confidence: 99%

3D Flow Simulation for Viscous Nonisothermal Incompressible Fluid in Injection Molding

Cao

Shen

Wang

2005

Polymer-Plastics Technology and Engineering

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The major drawbacks of the Hele-Shaw approximation, commonly used today as a means of simplifying the simulation of the injection molding process, are the inherent loss of the ability to predict important physical phenomena and the ambiguity involved in the definition of a midplane. With the objective of eliminating many of these problems, a fully three-dimensional mold filling simulation program has been developed. The governing equations are in terms of Navier-Stokes problems for the viscous, incompressible, nonisothermal, and non-Newtonian fluid. To avoid the simultaneous determination of the coupled velocity and pressure, this article introduces an iterative method that at any given time step solves the components independently. This method reduces memory needs in simulation and enhances the stability of numerical scheme. In addition, this article also presents a mixed implicit and ''up-wind'' scheme to discrete the energy equation. It can overcome the spatial oscillations of temperature in numerical simulation. Good agreements with both analytic solution and the actual processes are found in the current investigation. This method can successfully predict the flow features in injection molding.

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A Taylor discontinuous Galerkin method for the thermal solution in 3D mold filling

Cited by 30 publications

References 8 publications

Fractional Step Like Schemes for Free Surface Problems with Thermal Coupling Using the Lagrangian PFEM

Fractional Step Like Schemes for Free Surface Problems with Thermal Coupling Using the Lagrangian PFEM

Elastic flow-front fingering instability in flowing polymer solutions

3D Flow Simulation for Viscous Nonisothermal Incompressible Fluid in Injection Molding

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