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Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws

Lectures Presented at a Workshop at the Mathematical Research Institute Oberwolfach, Germany, Jan 15 – 21, 2012

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  • © 2013

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Editors:
  1. Rainer Ansorge

    1. , Department of Mathematics, University of Hamburg, Hamburg, Germany

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  2. Hester Bijl

    1. , Department of Aerospace Engineering, Delft University of Technology, Delft, Netherlands

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  3. Andreas Meister

    1. , Department of Mathematics and Natural Sc, University of Kassel, Kassel, Germany

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  4. Thomas Sonar

    1. Institute for Computational Mathematics, Technical University of Braunschweig, Braunschweig, Germany

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  • Up-to-date-information on high-order numerical methods
  • The book attracts students as well as professionals in that field of interest
  • Writtten by leading experts in the field

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM, volume 120)

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About this book

In January 2012 an Oberwolfach workshop took place on the topic of  recent

developments in the numerics of partial differential equations. Focus was  laid

on methods of high order and on applications in Computational Fluid Dynamics. The book covers most of the talks presented at this workshop.  

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Table of contents (19 chapters)

  1. Front Matter

    Pages 1-12
    Download chapter PDF

  2. A Second Order Accurate Kinetic Relaxation Scheme for Inviscid Compressible Flows

    • K. R. Arun, M. Lukáčová-Medvidová, Phoolan Prasad, S. V. Raghurama Rao
    Pages 1-24

  3. On One-Dimensional Low Mach Number Applications

    • Maria Bauer, Elisabetta Felaco, Ingenuin Gasser
    Pages 25-39

  4. High Order and Underresolution

    • Andrea Beck, Gregor Gassner, Claus-Dieter Munz
    Pages 41-55

  5. Solving Nonlinear Systems Inside Implicit Time Integration Schemes for Unsteady Viscous Flows

    • Philipp Birken
    Pages 57-71

  6. Discrete Flux-Corrected Transport: Numerical Analysis, Tensor-Valued Extension and Application in Image Processing

    • Michael Breuß, Bernhard Burgeth, Luis Pizarro
    Pages 73-87

  7. Quantification of Numerical and Physical Mixing in Coastal Ocean Model Applications

    • Hans Burchard, Ulf Gräwe
    Pages 89-103

  8. Dealing with Parasitic Behaviour in G-Symplectic Integrators

    • J. C. Butcher
    Pages 105-123

  9. An Adaptive Artificial Viscosity Method for the Saint-Venant System

    • Yunlong Chen, Alexander Kurganov, Minlan Lei, Yu Liu
    Pages 125-141

  10. Discontinuous Galerkin Method – A Robust Solver for Compressible Flow

    • Miloslav Feistauer, Jan Česenek, Václav Kučera
    Pages 143-160

  11. A Rigorous Application of the Method of Vertical Lines to Coupled Systems in Finite Element Analysis

    • Stefan Hartmann, Steffen Rothe
    Pages 161-175

  12. Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes

    • Willem Hundsdorfer, Anna Mozartova, Valeriu Savcenco
    Pages 177-195

  13. On the Construction of Kernel-Based Adaptive Particle Methods in Numerical Flow Simulation

    • Armin Iske
    Pages 197-221

  14. An Assessment of the Efficiency of Nodal Discontinuous Galerkin Spectral Element Methods

    • David A. Kopriva, Edwin Jimenez
    Pages 223-235

  15. Sub-cycling Strategies for Maritime Two-Phase Flow Simulations

    • Manuel Manzke, Jan-Patrick Voss, Thomas Rung
    Pages 237-251

  16. The DG Scheme on Triangular Grids with Adaptive Modal and Variational Filtering Routines Applied to Shallow Water Flows

    • Andreas Meister, Sigrun Ortleb
    Pages 253-266

  17. Enhanced Accuracy for Finite-Volume and Discontinuous Galerkin Schemes via Non-intrusive Corrections

    • Claus-Dieter Munz, Alexander Filimon, Michael Dumbser, Gregor Gassner
    Pages 267-282

  18. Linear and Nonlinear Boundary Conditions for Wave Propagation Problems

    • Jan Nordström
    Pages 283-299

  19. A New Stiffly Accurate Rosenbrock-Wanner Method for Solving the Incompressible Navier-Stokes Equations

    • Joachim Rang
    Pages 301-315

  20. On the Spectral Difference Method with Modal Filtering Applied to the Euler Equations

    • Thomas Sonar, Martina Wirz
    Pages 317-325
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Editors and Affiliations

  • , Department of Mathematics, University of Hamburg, Hamburg, Germany

    Rainer Ansorge

  • , Department of Aerospace Engineering, Delft University of Technology, Delft, Netherlands

    Hester Bijl

  • , Department of Mathematics and Natural Sc, University of Kassel, Kassel, Germany

    Andreas Meister

  • Institute for Computational Mathematics, Technical University of Braunschweig, Braunschweig, Germany

    Thomas Sonar

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