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    GRK 2583: Modeling, Simulation and Optimization of Fluid Dynamic Applications
    The RTG aims at the holistic education of junior scientists in the mathematical fields of Modeling, Simulation, and Optimization (MSO). The mathematical focus of the RTG is on mathematical modeling, adaptive discretization & approximation algorithms, mathematical data analysis, and shape optimization with PDEs. The RTG's research activities address challenging fluid dynamic problems, where they are inspired by Hamburgspecific applied sciences, such as climate research & meteorology, aerospace & marine engineering, or medicine. Our approach to next generation MSO is based on the leitmotif of the RTG: Mathematics drives applications while being inspired by applications. With this leitmotif the RTG carries forward and improves education and research in MSO by an inherent interdisciplinary approach, i.e., to stimulate fundamental education and research in MSOmathematics by highly complex applications and at the same time transfer tailored MSO-methods developed in mathematics to applied sciences. In this way, the RTG promotes an exchange of research paradigms between the participating disciplines and provides a modern approach to training in fundamental MSO-research for scientfically and socially relevant current problems. The RTG has a clear scientific focus with a well aligned educational profile. The leitmotif is implemented through nine thematically intertwined research topics, which combine aspects of MSOmathematics with an associated fluid dynamic application. Key technologies will jointly be developed and disseminated through lab-activities. Scientific exchange is facilitated and fostered through lecture series, research seminars, colloquia, annual retreats, and summer schools. The international networking of the RTG will benefit from a distinguished guest program involving a variety of world leading experts. The RTG will be hosted by the Lothar Collatz Center for Computing in Science. In particular, the RTG will be embedded in the well-established structures of the Lothar Collatz Graduate School. The academic platform of the RTG is enhanced by joining forces with established activities of the C3S and LCGS, e.g. the Lothar Collatz Seminar, and by contributing to the annual Plön Young Researcher Meeting & Workshop, and by the comprehensive course program of the Hamburg Research Academy (HRA, see Section. The educational program is based on long-standing collaborations of the involved researchers and institutions. The qualification concept is well connected to local and international educational programs that are jointly operated by the UHH and the TUHH. It reects shared experience on best practices and also supports our ambition for a rapid initial advancement as well as leadership skill promotion. Thus, the curriculum involves innovative training modules e.g. research management or entrepreneurship courses supplementary to the scientific education. With this approach the RTG is unique and will perform interdisciplinary research
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    SPP 1679: Subproject "Numerical solution methods for coupled population balance systems for the dynamic simulation of multivariate particle processes at the example of shape-selective crystallization"
    The goal of this project (six-year period) is the development of accurate and efficient methods for the numerical solution of multivariate population balance systems. As application problem, we consider an innovative shape-selective crystallization process. The final aim is the optimal process design and operation through the use of the developed numerical methods. In order to reach this goal, it is planned to develop and systematically compare techniques for the numerical treatment of the differential and integral operators appearing in population balance equations. These two types of operators are entirely different in their mathematical properties as well as in the appropriate numerical techniques for their solution. We establish benchmark problems which exhibit the desired behaviour of particle populations. These benchmarks are also realized experimentally. Through the experiments, reliable measured data become available which serve as reference values and support the evaluation of the numerical techniques. In the first project period, we closed gaps which existed concerning the evaluation of numerical techniques for the univariate case. In the second project period, we focus on the bivariate case (crystals with two internal properties), both in its experimental realization as well as in the development of suitable numerical methods and a subsequent systematic comparison of experimental and simulation results. In the third project period we plan to realize experimentally an integrated shape-selective crystallization process with several coupled process units and to simulate this process by using the developed numerical techniques. With this process we want to control the size and shape distribution of the crystal product. With respect to growth-dominated multivariate processes, improved algebraic stabilization schemes will be developed and used for the simulation of population balance systems in chemical engineering problems.Another aim of the third period is the numerical treatment of multivariate aggregation processes. It will be shown for uniform grids that aggregation integrals can be evaluated with linear costs by use of the Fast Fourier Transformation (FFT). This allows simulations on much finer grids than with conventional methods. The prerequisite for this approach is a separable approximation of the aggregation kernel - a property featured by many kernel functions of practical relevance.
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