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Full Description
This book describes recent collaborations combining the expertise of applied mathematicians, engineers and geophysicists within a research training group (RTG) on "Modeling, Simulation and Optimization of Fluid Dynamic Applications", funded by the Deutsche Forschungsgemeinschaft (DFG). The focus is on mathematical modeling, adaptive discretization, approximation strategies and shape optimization with PDEs.
The balanced research program is based on the guiding principle that mathematics drives applications and is inspired by applications. With this leitmotif the RTG advances research in Modeling, Simulation and Optimization by an interdisciplinary approach, i.e., to stimulate fundamental education and research by highly complex applications and at the simultaneously transfer tailored mathematical methods to applied sciences.
The reported research involves nine projects and addresses challenging fluid dynamic problems inspired by applied sciences, such as climate research & meteorology, energy, aerospace & marine engineering, or medicine. More fundamental research concerning analysis, approximation and numerics is also covered.
The material represents a successful attempt to exchange research paradigms between different disciplines and thus displays a modern approach to basic research into scientifically and societally relevant contemporary problems.
Contents
1. Lower Bounds for the Advection-Hyperdiffusion Equation.- 2. Modeling and Simulation of Parabolic Trough Collectors using Nanofluids.- 3. Adaptive DG Methods for 1D unsteady Convection-Diffusion Problems on a Moving Mesh.- 4. Anisotropic Kernels for Particle Flow Simulation.- 5. An Error-Based Low-Rank Correction for Pressure Schur Complement Preconditioners.- 6. Radon-based Image Reconstruction for MPI using a continuously rotating FFL.- 7. Numerical Simulation of an idealized coupled Ocean-Atmosphere Climate Model.- 8. Application of p-Laplacian relaxed steepest Descent to Shape Optimizations in two-phase Flows.- 9. Computing High-Order p-Harmonic Descent Directions and Their Limits in Shape Optimization.
