Modeling Simulation and Optimization of Fluid Dynamic Applications

✍ Scribed by Armin Iske; Thomas Rung; (eds.)

• Publisher: Springer Nature Switzerland
• Year: 2023
• Tongue: English
• Leaves: 165
• Series: Lecture Notes in Computational Science and Engineering
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Preface
Contents
Chapter 1 Lower Bounds for the Advection-Hyperdiffusion Equation
1.1 Introduction
1.2 Upper Bound for the Advection-Hyperdiffusion Equation
1.3 Lower Bound for the Advection-Hyperdiffusion Equation
1.3.1 Lower Bound for the Hyperdiffusion Equation
1.3.2 Upper Bound for the Perturbation
1.3.3 Lower Bound for the Energy
1.4 Lower Bounds on the Mixing Norms
1.4.1 Upper Bound for the Gradient of the Advection-Hyperdiffusion Equation
1.5 Conclusion
1.6 Appendix
Acknowledgment
References
Chapter 2 Modeling and Simulation of Parabolic Trough Collectors using Nanofluids: Application to NOOR I Plant in Ouarzazate, Morocco
2.1 Introduction
2.2 Mathematical Model
2.3 Numerical Simulation
2.4 Results and Discussion
2.5 Conclusions
Acknowledgment
References
Chapter 3 Adaptive Discontinuous Galerkin Methods for 1D unsteady Convection-Diffusion Problems on a Moving Mesh
3.1 Introduction
3.2 Flow map and interior penalty discretization
3.2.1 Model problem
3.2.2 Flow maps
3.2.3 Semi-discretization and function spaces
3.2.3.1 Notation and weak form
3.2.3.2 Bilinear forms and function spaces for the semi-discretization
3.3 Error bound for the stationary problem
3.4 Error bound for the semidiscrete nonstationary problem
3.5 Test case
3.6 Conclusion
Acknowledgment
References
Chapter 4 Anisotropic Kernels for Particle Flow Simulation
4.1 Introduction
4.2 The Finite Volume Particle Method
4.3 Kernel-based Reconstruction in Particle Flow Simulations
4.4 Reconstruction by Polyharmonic Splines
4.5 Reconstruction by Anisotropic Kernels
4.6 Numerical Examples and Comparisons
4.6.1 Anisotropic Kernels adapted to underlying Geometry
4.6.2 Data Point Selection
4.6.3 Anisotropic Kernels adapted to Particle Distribution
4.6.4 Numerical Comparisons
4.7 Outlook
Acknowledgment
References
Chapter 5 An Error-Based Low-Rank Correction for Pressure Schur Complement Preconditioners
5.1 Introduction
5.1.1 Model
5.1.2 The initial preconditioner
5.2 Error-based low-rank correction
5.2.1 Construction of the update
5.2.2 Analysis of the remainder
5.2.3 Repeated updates
5.3 Complexity
5.4 Numerical results
5.4.1 Action on the eigenvalues
5.4.2 Convergence
5.5 Outlook
Data Availability
Acknowledgment
References
Chapter 6 Radon-based Image Reconstruction for MPI using a continuously rotating FFL
6.1 Introduction
6.2 Field-free Line Magnetic Particle Imaging
6.3 Relation of the MPI Forward Operator to the Radon Transform
6.4 TV regularized Image Reconstruction
6.5 Numerical Results
6.6 Conclusion
Acknowledgment
References
Chapter 7 Numerical Simulation of an idealized coupled Ocean-Atmosphere Climate Model
7.1 Introduction
7.2 Idealized ocean model
7.3 Idealized atmosphere model
7.4 Climate model
7.5 Conclusions and future work
Acknowledgement
References
Chapter 8 Application of p-Laplacian relaxed Steepest Descent to Shape Optimizations in Two-Phase Flows
8.1 Introduction
8.2 Mathematical Model
8.3 Computational Model
8.4 Numerical Results
8.5 Summary
Acknowledgements
Replication of results
References
Chapter 9 Harmonic Descent Directions and Their Limits in Shape Optimization
9.1 Introduction
9.2 High-Order
9.3 Numerical Results
9.4 Descent inW1,8
9.5 Conclusion
Acknowledgment
References

✦ Subjects

Mathematics and Statistics; Computational Science and Engineering; Computational Mathematics and Numerical Analysis