t8code - scalable and modular adaptive mesh refinement

t8code is a versatile open source library for parallel adaptive mesh refinement on hybrid meshes. [1] It is exascale-ready and capable of efficiently managing meshes with up to a trillion elements distributed on a million of cores as already shown in a peer-reviewed research paper. [2] On the top-level, t8code uses forests of trees to represent unstructured meshes with complex geometries. Space-filling curves index individual elements within a forest, which requires only minimal amounts of memory allowing for efficient and scalable algorithms of mesh management. In contrast to existing solutions, t8code has the capability to manage an arbitrary number of tetrahedra, hexahedra, prisms and pyramids within the same mesh. With this poster we want to present the first official release (v1.0) of our software and give a quick overview over its main features. Besides presenting the core algorithms of t8code, we give application scenarios on how our library integrates into major simulation frameworks for weather forecasting, climate modeling and engineering; and how they benefit from our approach to do AMR. [1] https://github.com/DLR-AMR/t8code [2] https://epubs.siam.org/doi/abs/10.1137/20M138303

Using the constant properties model for accurate performance estimation of thermoelectric generator elements

Thermoelectric devices convert thermal energy directly into electrical energy or vice versa. Analytically, the performance (efficiency and power output) of a thermoelectric generator can be quickly estimated using a Constant Properties Model (CPM) suggested by Ioffe. However, material properties in general are temperature dependent and the CPM can yield meaningful estimates only if the constant values of the TE properties used in the formulations are physically appropriate. In this study, a comparison of different averaging modes shows that a combination of integral averaging over the temperature scale for the Seebeck coefficient and spatial averages for the electrical and thermal resistivities proves to be the best among the considered approximations to represent the constant property values. However, averaging spatially requires the knowledge of the exact temperature distribution along the length of the thermoelectric leg (temperature profile), which is usually obtained by Finite Element Method (FEM) calculations. Since FEM is costly and time consuming, a fast and easy way of obtaining a well approximated self-consistent temperature profile is used in this study. The relevance, magnitude and the physical origin of the non-linearity of the temperature profile are visualised by separately plotting the individual contributions to the bending of the temperature profile (Joule, Thomson and Fourier heat contributions). On analyzing the temperature profiles for different highly efficient thermoelectric materials, it is found that the non-constancy of the temperature dependence of the thermal conductivity significantly contributes to the deflection of real temperature profiles from a linear one. This mainly explains the considerable discrepancy of CPM results from exact calculations whereas, so far, the neglect of Thomson heat has been assumed to be the main source of discrepancy and several models with Thomson correction factors have been proposed. With our current view, such models cannot completely remove the discrepancy to CPM unless the T profile is taken into account and can lead to unpredictable error for different material cases and temperatures