Finite element solution of the 3D mold filling problem for viscous incompressible fluid Original Research Article

A general solution for the 3D mold filling by incompressible viscous fluid is described. It is based on the combination of an extended flow solver and the solution of a transport equation governing the flow front position. The flow solver uses tetrahedral elements, a first order stable mixed velocity pressure formulation entering in the family of the MINI-element, and a global iterative solution. The characteristic function of the fluid domain is shown to follow a conservative law and the moving fluid description is transformed into a transport equation in the whole domain to be filled. An explicit discontinuous Taylor-Galerkin scheme is introduced to solve this fluid motion equation. This scheme is shown to be consistent and conservative. The calculated shape of the fountain flow front is compared to the reference one. The flexibility and the robustness of this approach is demonstrated through complicated flows and geometries examples.