Table Of ContentSpringer Proceedings in Mathematics & Statistics
Christian Klingenberg
Editors
Michael Westdickenberg
Theory, Numerics
and Applications
of Hyperbolic
Problems II
Aachen, Germany, August 2016
Springer Proceedings in Mathematics & Statistics
Volume 237
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Christian Klingenberg Michael Westdickenberg
(cid:129)
Editors
Theory, Numerics
and Applications
of Hyperbolic Problems II
Aachen, Germany, August 2016
123
Editors
Christian Klingenberg Michael Westdickenberg
Department ofMathematics Department ofMathematics
Würzburg University RWTH Aachen University
Würzburg Aachen
Germany Germany
ISSN 2194-1009 ISSN 2194-1017 (electronic)
SpringerProceedings in Mathematics& Statistics
ISBN978-3-319-91547-0 ISBN978-3-319-91548-7 (eBook)
https://doi.org/10.1007/978-3-319-91548-7
LibraryofCongressControlNumber:2018941540
Mathematics Subject Classification (2010): 35Lxx, 35M10, 35Q30, 35Q35, 35Q60, 35Q72, 35R35,
65Mxx,65Nxx,65Txx,65Yxx,65Z05,74B20,74Jxx,76L06,76Rxx,76Txx,80A32,80Mxx,83C55,
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Contents
A Stochastic Galerkin Method for the Fokker–Planck–Landau
Equation with Random Uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Jingwei Hu, Shi Jin and Ruiwen Shu
On Robust and Adaptive Finite Volume Methods for Steady
Euler Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Guanghui Hu, Xucheng Meng and Tao Tang
The Burgers–Hilbert Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
John K. Hunter
General Linear Methods for Time-Dependent PDEs . . . . . . . . . . . . . . . 59
Alexander Jaust and Jochen Schütz
An Invariant-Region-Preserving (IRP) Limiter to DG Methods
for Compressible Euler Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Yi Jiang and Hailiang Liu
b-Schemes with Source Terms and the Convergence Analysis . . . . . . . . 85
Nan Jiang
Existence of Undercompressive Shock Wave Solutions
to the Euler Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Buğra Kabil
Some Numerical Results of Regional Boundary Controllability
with Output Constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Touria Karite, Ali Boutoulout and Fatima Zahrae El Alaoui
Water Hammer Modeling for Water Networks via Hyperbolic PDEs
and Switched DAEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Rukhsana Kausar and Stephan Trenn
Stability Criteria for Some System of Delay Differential Equations . . . . 137
Yuya Kiri and Yoshihiro Ueda
v
vi Contents
Bound-Preserving Reconstruction of Tensor Quantities for Remap
in ALE Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Matej Klima, Milan Kucharik, Mikhail Shashkov and Jan Velechovsky
On Computing Compressible Euler Equations with Gravity . . . . . . . . . 159
Christian Klingenberg and Andrea Thomann
On Well-Posedness for a Multi-particle Fluid Model . . . . . . . . . . . . . . . 167
Christian Klingenberg, Jens Klotzky and Nicolas Seguin
On Quantifying Uncertainties for the Linearized BGK Kinetic
Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Christian Klingenberg, Qin Li and Marlies Pirner
Kinetic ES-BGK Models for a Multi-component Gas Mixture. . . . . . . . 195
Christian Klingenberg, Marlies Pirner and Gabriella Puppo
An Arbitrary Lagrangian–Eulerian Discontinuous Galerkin Method
for Conservation Laws: Entropy Stability . . . . . . . . . . . . . . . . . . . . . . . 209
Christian Klingenberg, Gero Schnücke and Yinhua Xia
Simplified Hyperbolic Moment Equations . . . . . . . . . . . . . . . . . . . . . . . 221
Julian Koellermeier and Manuel Torrilhon
Weakly Coupled Systems of Conservation Laws
on Moving Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Andrea Korsch
A Phase-Field Model for Flows with Phase Transition. . . . . . . . . . . . . . 243
Mirko Kränkel and Dietmar Kröner
MathematicalTheoryofTwo-PhaseGeochemicalFlowwithChemical
Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
W. J. Lambert, A. C. Alvarez, D. Marchesin and J. Bruining
Localization of Adiabatic Deformations in Thermoviscoplastic
Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Min-Gi Lee, Theodoros Katsaounis and Athanasios E. Tzavaras
The Global Nonlinear Stability of Minkowski Spacetime
for Self-gravitating Massive Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
Philippe G. LeFloch
A Particle-Based Multiscale Solver for Compressible Liquid–Vapor
Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
Jim Magiera and Christian Rohde
Lp-Lq Decay Estimates for Dissipative Linear Hyperbolic Systems
in 1D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
Corrado Mascia and Thinh Tien Nguyen
Contents vii
A Numerical Approach of Friedrichs’ Systems Under Constraints
in Bounded Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
Clément Mifsud and Bruno Després
Lagrangian Representation for Systems of Conservation Laws:
An Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
Stefano Modena
Kinematical Conservation Laws in Inhomogeneous Media. . . . . . . . . . . 349
S. Baskar, R. Murti and P. Prasad
ArtificialViscosityforCorrectionProcedureviaReconstructionUsing
Summation-by-Parts Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
Jan Glaubitz, Philipp Öffner, Hendrik Ranocha and Thomas Sonar
On a Relation Between Shock Profiles and Stabilization Mechanisms
in a Radiating Gas Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
Masashi Ohnawa
On the Longtime Behavior of Almost Periodic Entropy Solutions
to Scalar Conservation Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
Evgeny Yu. Panov
Structure Preserving Schemes for Mean-Field Equations
of Collective Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
Lorenzo Pareschi and Mattia Zanella
A Numerical Model for Three-Phase Liquid–Vapor–Gas Flows
with Relaxation Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
Tore Flåtten, Marica Pelanti and Keh-Ming Shyue
Feedback Stabilization of a Linear Fluid–Membrane System
with Time Delay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
Gilbert Peralta
A Unified Hyperbolic Formulation for Viscous Fluids
and Elastoplastic Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
Michael Dumbser, Ilya Peshkov and Evgeniy Romenski
On the Transverse Diffusion of Beams of Photons
in Radiation Therapy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465
S. Brull, B. Dubroca, M. Frank and T. Pichard
Numerical Viscosity in Large Time Step HLL-Type Schemes . . . . . . . . 479
Marin Prebeg
Correction Procedure via Reconstruction Using
Summation-by-Parts Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
Philipp Öffner, Hendrik Ranocha and Thomas Sonar
viii Contents
A Third-Order Entropy Stable Scheme for the Compressible Euler
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
Deep Ray
Did Numerical Methods for Hyperbolic Problems
Take a Wrong Turning? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
Philip Roe
Astrophysical Fluid Dynamics and Applications
to Stellar Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
Friedrich K. Röpke
Nonlinear Stability of Localized and Non-localized Vortices
in Rotating Compressible Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549
Olga S. Rozanova and Marko K. Turzynsky
Coupled Scheme for Hamilton–Jacobi Equations. . . . . . . . . . . . . . . . . . 563
Smita Sahu
Compressible Heterogeneous Two-Phase Flows . . . . . . . . . . . . . . . . . . . 577
Nicolas Seguin
Bound-Preserving High-Order Schemes for Hyperbolic Equations:
Survey and Recent Developments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
Chi-Wang Shu
Comparison of Shallow Water Models for Rapid Channel Flows . . . . . 605
Stefanie Elgeti, Markus Frings, Anne Küsters, Sebastian Noelle
and Aleksey Sikstel
On Stability and Conservation Properties of (s)EPIRK Integrators
in the Context of Discretized PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617
Philipp Birken, Andreas Meister, Sigrun Ortleb and Veronika Straub
Compactness on Multidimensional Steady Euler Equations . . . . . . . . . . 631
Tian-Yi Wang
A Constraint-Preserving Finite Difference Method for the Damped
Wave Map Equation to the Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643
Franziska Weber
Integral Transform Approach to Solving Klein–Gordon Equation
with Variable Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655
Karen Yagdjian
AsymptoticConsistencyoftheRS-IMEXSchemefortheLow-Froude
Shallow Water Equations: Analysis and Numerics. . . . . . . . . . . . . . . . . 665
Hamed Zakerzadeh
Contents ix
Class of Space–Time Entropy Stable DG Schemes for Systems
of Convection–Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677
Georg May and Mohammad Zakerzadeh
Invariant Manifolds for a Class of Degenerate Evolution Equations
and Structure of Kinetic Shock Layers . . . . . . . . . . . . . . . . . . . . . . . . . 691
Kevin Zumbrun
