Lightweight fiber-reinforced injection molding parts play a crucial role in reducing energy consumption, for example, in mobility applications. In order to develop a product-aware production cycle for fiber-reinforced plastics (FRP), accurate high-fidelity simulations are required. In addition to the simulation of the molten polymer, a fiber orientation model needs to be considered. This not only allows the final fiber orientation in the solidified part to be determined, but also affects the flow field [1]. The well-known Folgar-Tucker model in its tensor form, proposed by Advani and Tucker, is employed here to solve for the orientation of short fibers [2, 3]. Furthermore, to consider the fiber orientation results to be physically admissible, the fiber orientation tensor has to be positive semidefinite and have a unit trace [4]. However, these properties are not automatically fulfilled in a simulation. To obtain a conservative and physically admissible solution, flux correction schemes can be employed [4]. Another option is to choose an appropriate closure and adapt the time step size in an a posteriori step, as recommended by Lohmann [4]. To ensure an accurate and efficient simulation, we employ a simplex space-time finite element formulation to solve the melt flow, as proposed in [5]. For the orientation tensor, Redjeb et al. [6] used a prismatic space-time approach. We employ a simplex space-time formulation which allows for local refinement in space and time on conforming meshes. We also propose a new adaptive local space-time refinement procedure driven by a heuristic a posteriori error estimator, based on whether the properties of the orientation tensor are admissible or not, helping to maintain physical results and reduce discretization errors. The simplex space-time discretization and error estimator are then investigated using test cases. [1] B. E. Verweyst, C. L. Tucker III, The Canadian Journal of Chemical Engineering, 2002. [2] F. Folgar, C. L. Tucker III, Journal of Reinforced Plastics and Composites, 1984. [3] S. G. Advani, C. L. Tucker III, Journal of Rheology, 1987. [4] C. Lohmann, Physics-compatible finite element methods for scalar and tensorial advection problems, 1, Wiesbaden, Springer Fachmedien, 2019. [5] V. Karyofylli, L. Wendling, M. Make, N. Hosters, M. Behr, Computers & Fluids, 2019. [6] A. Redjeb, Dissertation, École Nationale Supérieure des Mines de Paris, 2007