Engineering design via CAD software relies on Non-Uniform Rational B-Splines (NURBS) as a means for representing and communicating geometry. Therefore, in general, a NURBS description of a given design can be considered the exact description. The development of isogeometric methods has made the geometry available to analysis methods [1]. Isogeometric analysis has been particularly successful in structural analysis; one reason being the wide-spread use of two-dimensional finite elements in this field. For fluid dynamics, where three-dimensional analysis is usually indispensable, isogeometric methods are more complicated, yet of course not impossible, to apply in a general fashion. This paper describes a method that enables the solution of fluid-structure-interaction with a matching spline description of the interface. On the structural side, the spline is used in an isogeometric setting. On the fluid side, the same spline is used in the framework of a NURBS-enhanced finite element method (extension of [2]). The coupling of the structural and the fluid solution is greatly facilitated by the common spline interface. The use of the identical spline representation for both sides permits a direct transfer of the necessary quantities, all the while still allowing an adjusted, individual refinement level for both sides.
We present a boundary-conforming space-time finite element method to compute the flow inside co-rotating, self-wiping twin-screw extruders. The mesh update is carried out using the newly developed Snapping Reference Mesh Update Method (SRMUM). It allows to compute time-dependent flow solutions inside twinscrew extruders equipped with conveying screw elements without any need for re-meshing and projections of solutions -making it a very efficient method. We provide cases for Newtonian and non-Newtonian fluids in 2D and 3D, that show mesh convergence of the solution as well as agreement to experimental results. Furthermore, a complex, unsteady and temperature-dependent 3D test case with multiple screw elements illustrates the potential of the method also for industrial applications.
The idea our global polity is chiefly divided by territorially organized nation‐states captures contemporary constellations of power and authority only insufficiently. Through a decoupling of power and the state, political spaces no longer match geographical spaces. Instead of simply acknowledging a challenge to the state, there is the need to rethink the changing meaning of space for political processes. The paper identifies three aspects, a reconceptualization of the spatial assumptions that IR needs to address: the production of space, the constitutive role of boundaries, and the problem of order. With this contribution, we argue that one avenue in understanding the production of space and the following questions of order is by converging systems theory and critical geopolitics. While the latter has already developed a conceptual apparatus to analyze the production of space, the former comes with an encompassing theoretical background, which takes “world society” as the starting point of analysis. In this respect, nation states are understood as a form of internal differentiation of a wider system, namely world society.
This paper presents a novel spline-based meshing technique that allows for usage of boundary-conforming meshes for unsteady flow and temperature simulations in co-rotating twin-screw extruders. Spline-based descriptions of arbitrary screw geometries are generated using Elliptic Grid Generation. They are evaluated in a number of discrete points to yield a coarse classical mesh. The use of a special control mapping allows to fine-tune properties of the coarse mesh like orthogonality at the boundaries. The coarse mesh is used as a 'scaffolding' to generate a boundary-conforming mesh out of a fine background mesh at run-time. Storing only a coarse mesh makes the method cheap in terms of memory storage. Additionally, the adaptation at run-time is extremely cheap compared to computing the flow solution. Furthermore, this method circumvents the need for expensive re-meshing and projections of solutions making it efficient and accurate. It is incorporated into a space-time finite element framework. We present time-dependent test cases of non-Newtonian fluids in 2D and 3D for complex screw designs. They demonstrate the potential of the method also for arbitrarily complex industrial applications.
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