A Taylor discontinuous Galerkin method for the thermal solution in 3D mold filling
Résumé
In continuity with the work of the authors, a Taylor discontinuous Galerkin method is introduced to solve the thermal problem in the context of the 3D mold filling by viscous incompressible fluid. This numerical scheme is designed to deal with the physical phenomena of shear and temperature dependent viscosity, viscous heat generation and heat transfer by conduction and convection. A mixed temperature/heat flux formulation is introduced which enables to capture high temperature gradients without any polluting oscillations of the solution. The temperature and the heat flux are interpolated by a constant per element (P0 element) and an explicit solution based on the recursive time derivation of the equations is described. This approach aims to simulate non-isothermal flows of viscous fluid with moving free surfaces and more particularly the injection molding process involving thermal shocks at the interface between the cold mold wall and the hot polymer. The extension of the method in the context of the mold filling problem is given and several examples are proposed. The thermal solver is coupled to the mechanical solver which is based on a first order mixed finite element method for the kinematic and the solution of a transport equation for the flow front motion description. The proposed 3D technic is validated with known solutions and it is compared to 2D calculation obtained by different approaches. In continuity with the work of the authors, a Taylor discontinuous Galerkin method is introduced to solve the thermal problem in the context of the 3D mold filling by viscous incompressible fluid. This numerical scheme is designed to deal with the physical phenomena of shear and temperature dependent viscosity, viscous heat generation and heat transfer by conduction and convection. A mixed temperature/heat flux formulation is introduced which enables to capture high temperature gradients without any polluting oscillations of the solution. The temperature and the heat flux are interpolated by a constant per element (P0 element) and an explicit solution based on the recursive time derivation of the equations is described. This approach aims to simulate non-isothermal flows of viscous fluid with moving free surfaces and more particularly the injection molding process involving thermal shocks at the interface between the cold mold wall and the hot polymer. The extension of the method in the context of the mold filling problem is given and several examples are proposed. The thermal solver is coupled to the mechanical solver which is based on a first order mixed finite element method for the kinematic and the solution of a transport equation for the flow front motion description. The proposed 3D technic is validated with known solutions and it is compared to 2D calculation obtained by different approaches.