Physics-Compatible Finite Element Methods for Scalar and Tensorial Advection Problems (PDF)

Christoph Lohmann introduces a very general framework for the analysis and design of bound-preserving finite element methods. The results of his in-depth theoretical investigations lead to promising new extensions and modifications of existing algebraic flux correction schemes. The main focus is on new limiting techniques designed to control the range of solution values for advected scalar quantities or the eigenvalue range of symmetric tensors. The author performs a detailed case study for the Folgar-Tucker model of fiber orientation dynamics. Using eigenvalue range preserving limiters and admissible closure approximations, he develops a physics-compatible numerical algorithm for this model.

Contents

• Equations of Fluid Dynamics
• Finite Element Discretization
• Limiting for Scalars
• Limiting for Tensors
• Simulation of Fiber Suspensions

Target Groups

• Researchers and students in the field of applied mathematics
• Developers of numerical methods for transport equations and of general-purpose simulation software for computational fluid dynamics, engineers in the field of fiber suspension flows and injection molding processes

The Author

Christoph Lohmann is a postdoctoral researcher in the Department of Mathematics at TU Dortmund University. His research activities are focused on numerical analysis of finite element methods satisfying discrete maximum principles.