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

✍ Scribed by Christoph Lohmann

• Publisher: Springer Fachmedien Wiesbaden;Springer Spektrum
• Year: 2019
• Tongue: English
• Leaves: 289
• Edition: 1st ed. 2019
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Mathematics; Computational Mathematics and Numerical Analysis; Numerical and Computational Physics, Simulation; Applications of Mathematics