Summary Employing simplex space‐time meshes enlarges the scope of compressible flow simulations. The simultaneous discretization of space and time with simplex elements extends the flexibility of unstructured meshes from space to time. In this work, we adapt a finite element formulation for compressible flows to simplex space‐time meshes. The method obtained allows, for example, flow simulation on spatial domains that change topology with time. We demonstrate this with the two‐dimensional simulation of compressible flow in a valve that fully closes and opens again. Furthermore, simplex space‐time meshes facilitate local temporal refinement. A three‐dimensional transient simulation of blow‐by past piston rings is run in parallel on 120 cores. The timings point out savings of computation time gained from local temporal refinement in four‐dimensional space‐time meshes.

Summary In this paper, we present the numerical solution of 2‐phase flow problems of engineering significance with a space‐time finite element method that allows for local temporal refinement. Arbitrary temporal refinement is applied to preselected regions of the mesh and is governed by a quantity that is part of the solution process, namely, the interface position in 2‐phase flow. Because of local effects such as surface tension, jumps in material properties, etc, the interface can in general be considered a region that requires high flexibility and high resolution, both in space and in time. The new method, which leads to tetrahedral (for 2D problems) and pentatope (for 3D problems) meshes, offers an efficient yet accurate approach to the underlying 2‐phase flow problems.

The quality of plastic parts produced through injection molding depends on many factors. Especially during the filling stage, defects such as weld lines, burrs, or insufficient filling can occur. Numerical methods need to be employed to improve product quality by means of predicting and simulating the injection molding process. In the current work, a highly viscous incompressible non-isothermal two-phase flow is simulated, which takes place during the cavity filling. The injected melt exhibits a shear-thinning behavior, which is described by the Carreau-WLF model. Besides that, a novel discretization method is used in the context of 4D simplex space-time grids [2]. This method allows for local temporal refinement in the vicinity of, e.g., the evolving front of the melt [10]. Utilizing such an adaptive refinement can lead to locally improved numerical accuracy while maintaining the highest possible computational efficiency in the remaining of the domain. For demonstration purposes, a set of 2D and 3D benchmark cases, that involve the filling of various cavities with a distributor, are presented.

Mold filling is an important stage of injection molding, which is one of the most commonly used manufacturing processes for the production of thermoplastic components in high volumes. As a consequence, the numerical simulation of this process based on computational fluid dynamics (CFD) is of great significance for production engineering [1,2]. However, modeling of the mold filling is a tremendously demanding process, when considering interfacial physical phenomena, such as two-phase flows, building a sharp interface between the molten plastics and the present air in the cavity or the dynamic wetting contact line at the cavity surface. A method for dealing with these phenomena is a local mesh refinement both in space and time. In this paper, the numerical solution of a mold filling problem using simplex-type space-time finite elements is presented and compared with experiments. These elements can be suited to increase efficiency, when used for the aforementioned refinement. In addition, a Navier's slip boundary condition is applied to the solid boundaries of the mold allowing the contact line to evolve along the boundary, while enabling a better prediction of the pressure distribution. The presented work was performed in collaboration of the subprojects B3 and B5 of the collaborative research center 1120 "Precision Melt Engineering".Keywords: Injection molding / Navier's slip boundary condition / simplex elements / space-time elements / two-phase flow Die Formfü llung ist ein wichtiger Vorgang des Spritzgießens, das eines der hä ufigsten verwendeten Verfahren zur Herstellung thermoplastischer Bauteile in hohen Stü ckzahlen ist. Infolgedessen ist die numerische Simulation dieses Prozesses auf der Grundlage der numerischen Strö mungsmechanik von großer Bedeutung fü r die Produktionstechnik [1,2]. Allerdings ist die Modellierung des Fü llvorgangs ein anspruchsvoller Prozess, wenn die komplexen physikalischen Phä nomene, wie die Zweiphasenströ mung, mit einem Interface zwischen der flü ssigen Kunststoffformmasse und der vorliegenden Luft oder die Kontaktlinie zwischen Formmasse und Kavitä tsoberflä che berü cksichtigt werden mü ssen. Eine Mö glichkeit, dies zu erreichen, ist eine lokale Netzverfeinerung in Raum und Zeit. In dieser Arbeit wird die numerische Lö sung des Fü llvorgangs eines plattenfö rmigen Formteils mittels Simplex Raum-Zeit-Gittern prä sentiert und mit experimentellen Ergebnissen vergli-Corresponding author:

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