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

Description

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. Front Matter ....Pages I-XII Introduction (Christoph Lohmann)....Pages 1-13 Equations of fluid dynamics (Christoph Lohmann)....Pages 15-34 Discretization (Christoph Lohmann)....Pages 35-52 Limiting for scalars (Christoph Lohmann)....Pages 53-149 Limiting for tensors (Christoph Lohmann)....Pages 151-210 Simulation of fiber suspensions (Christoph Lohmann)....Pages 211-261 Conclusions (Christoph Lohmann)....Pages 263-269 Back Matter ....Pages 271-283