Formulating 3D transient flow problems in a space-time setting results in a 4D problem. When discretized with one combined space-time mesh, we obtain a 4D mesh. These large meshes offer opportunities and pose challenges, both conceptually and computationally. First of all, local refinement in space and time can be exploited in simplex space-time meshes based on a-priori knowledge about the expected flow field [1]. Furthermore, in combination with a scalable preconditioner and linear solver, space-time formulations can open up a path to parallel-in-time computations and enable the efficient use of high-performance computing (HPC) infrastructures accessible to most computational mechanics institutes for research projects. In contrast, there is also a large demand for solutions to flow problems in settings with very limited computational power available. E.g., in the context of digital twins, fast-to-evaluate models are required to interact with sensor data of the real system under consideration. To address this issue, a reduced-order model (ROM) is derived with a projection-based Model Order Reduction (MOR) approach for deforming domain problems based on space-time finite elements [2]. Application cases include heat flux and advection-diffusion problems, as well as compressible and incompressible flows through a valve-like geometry and through the geometry of a clamped artery [3]. REFERENCES [1] M. von Danwitz, V. Karyofylli, N. Hosters, M. Behr, Simplex space-time meshes in compressible flow simulations. Int J Numer Meth Fluids, 91:29–48, 2019. [2] F. Key, F. Ballarin, S. Eusterholz, S. Elgeti, G. Rozza, Reduced flow model for plastics melt inside an extrusion die. Proc Appl Math Mech, 21(1):e202100071, 2021. [3] M. von Danwitz, P. Antony, F. Key, N. Hosters, M. Behr, Four-dimensional elastically deformed simplex space-time meshes for domains with time-variant topology. Int J Numer Meth Fluids, 93(12):3490–3506, 2021.