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

  • Book
  • © 2019

Overview

Authors:
  1. Christoph Lohmann

    1. Dortmund, Germany

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  • Foundations of Property-Preserving Flow Simulation

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XII
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  2. Introduction

    • Christoph Lohmann
    Pages 1-13

  3. Equations of fluid dynamics

    • Christoph Lohmann
    Pages 15-34

  4. Discretization

    • Christoph Lohmann
    Pages 35-52

  5. Limiting for scalars

    • Christoph Lohmann
    Pages 53-149

  6. Limiting for tensors

    • Christoph Lohmann
    Pages 151-210

  7. Simulation of fiber suspensions

    • Christoph Lohmann
    Pages 211-261

  8. Conclusions

    • Christoph Lohmann
    Pages 263-269

  9. Back Matter

    Pages 271-283
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Keywords

About this book

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.

Authors and Affiliations

  • Dortmund, Germany

    Christoph Lohmann

About 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.

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