雙曲問題：理論、數值方法及應用(第二卷)（簡體書）

《雙曲問題:理論、數值方法及應用(第2卷)》由高等教育出版社出版。

Volume 2
Contributed Talks
Alina Chertock, Jian-Guo Liu, Terrance Pendleton
Convergence Analysis of the Particle Method for the Camassa-Holm Equation
Paolo Corti
Stable Numerical Scheme for the Magnetic Induction Equation with Hall Effect
Andreas Dedner, Christoph Gersbacher
A Local Discontinuous Galerkin Discretization for Hydrostatic Free Surface Flows Using σ-transformed Coordinates
Donatella Donatelli, Pierangelo Marcati
Analysis of Quasineutral Limits
Renjun Duan, Robert M. Strain
On the Full Dissipative Property of the Vlasov-Poisson-Boltzmann System
P. Engel, C. Rohde
On the Space-Time Expansion Discontinuous Galerkin Method
Ulrik Skre Fjordholm
Energy Conservative and Stable Schemes for the Two-layer Shallow Water Equations
Jan Giesselmann
Sharp Interface Limits for Korteweg Models
Nan Jiang
On the Convergence of Semi-discrete High Resolution Schemes with Superbee Flux Limiter for Conservation Laws
Song Jiang, Qiangchang Ju, Fucai Li
Asymptotic Limits of the Compressible Magnetohydrodynamic Equations
Chunhua Jin, Tong Yang, Jingxue Yin
Waiting Time for a Non-Newtonian Polytropic Filtration Equation with Convection
Quansen Jiu, Yi Wang, Zhouping Xin
Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-dependent Viscosity
E. A. Johnson, J. A. Rossmanith
Ten-moment Two-fluid Plasma Model Agrees Well with PIC/Vlasov in GEM Problem
Frederike Kissling, Christian Rohde
Numerical Simulation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method
Ujjwal Koley
Implicit Finite Difference Scheme for the Magnetic Induction Equation
Anastasia Korshunova, Olga Rozanova
On Effects of Stochastic Regularization for the Pressureless Gas Dynamics
Dietmar Kroener
Jump Conditions across Phase Boundaries for the Navier-Stokes Korteweg system
Kai Krycki, Martin Frank
Numerical Treatment of a Non-classical Transport Equation Modelling Radiative Transfer in Atmospheric Clouds
Harish Kumar
Finite Volume Methods for the Two-fluid MHD Equations
Tong Li, Zhi-An Wang
Nonlinear Stability of Large Amplitude Traveling Waves to Hyperbolic-parabolic System Modeling Chemotaxis
Yong Li, Song Jiang, Qiangchang Ju, Hailiang Li
Quasi-neutral Limits of the Two-fluid Euler-Poisson Systems Qiuhua Liang
Dynamically Adaptive Simulation of Solute Transport Driven by Shallow Flows
Chunjin Lin
Asymptotic Stability of Rarefaction Waves in Radiative Hydrodynamics
Jun Luo, Kun Xu
A Symplecticity-preserving Gas-kinetic Scheme for Hydrodynamic Equations under External Forcing Field
Andrea Mentrelli, Tommaso Ruggeri, Masaru Sugiyama, Nanrong Zhao
Shock Wave Admissibility and Shock-induced Phase Transitions in a van der Waals Fluid
Magali Mercier
L1 Stability for Scalar Balance Laws; Application to Pedestrian Traffic
Gino Montecinos, Eleuterio Toro
Solver for the Generalized Riemann Problem for Balance Laws with Stiff Source Terms: The Scalar Case
Thomas Mueller, Dietmar Kroener
Related Problems for TV-estimates for Conservation Laws on Surfaces
Maria Luz Munoz-Ruiz, Carlos Parés Madronal
Properties of Path-conservative Schemes for Hyperbolic Systems of Balance Laws
Martin Nolte
A Fast Sweeping Method for Computing the Effective Hamiltonian Martina Pawlak, Thomas Sonar
A Spectral Difference Method with Dubiner Polynomials on Triangulations
G. Puppo, M. Semplice
Adaptive Grids and the Entropy Error Indicator
Xiaohong Qin, Yi Wang
Large-time Behavior of Solutions to the Inflow Problem of Full Compressible Navier-Stokes Equations
Peng Qu
Mechanism of Singularity Formation for Linearly Degenerate Quasilinear Hyperbolic Systems
Olivier Rouch, Paul Arminjon
Extension of Harten's Artificial Compression Method and of an Entropy-based Detector of Discontinuity to Unstructured Triangular Grids, using Arminjon-Viallon's Staggered Central Scheme
Roman Semenko
Layered Structures: Instability of the Shock Waves and Elecrtodynamical Instability
Zhi-Qiang Shao
Global Classical Discontinuous Solutions to the Generalized Riemann Problem for Linearly Degenerate Hyperbolic Conservation
Laws under Small BV Perturbations of the Initial Data
V. M. Shelkovich
One Class of Systems of Conservation Laws Admitting Delta-shocks
Wen Shen, Tianyou Zhang
A Conservation Law with Nonlocal Flux for Erosion Profiles Keh-Ming Shyue
A Moving-mesh Relaxation Scheme for One-dimensional Barotropic Two-phase Flow with Cavitation
Yuri Trakhinin
Well-posedness of the Free Boundary Problem for Non-relativistic and Relativistic Compressible Euler Equations with a Vacuum Boundary Condition
Yoshihiro Ueda
Convergence Rate to the Stationary Waves for Viscous Conservation Laws with Non-convexity on the Half Space
M. A. Ullah, Wenbin Gao, De-Kang Mao
Numerical Simulation of Shock-bubble Interactions Using Conservative Front Tracking Method
Jing Wang, Feng Xie
Asymptotic Stability of Viscous Contact Wave for the 1D Radiation Hydrodynamics System
Kung-Chien Wu, Chi-Kun Lin
Dispersive Limits of the Nonlinear Klein-Gordon Equation
Hao Yan, Li Chen
Semiclassical Limit of Quantum Semiconductor Models
Penghong Zhong, Shu Wang, Ke Wang, Ronghui Yang
A Result on Global Solutions to 3D Complex Ginzburg-Landau Equation
Penghong Zhong, Shu Wang, Ke Wang, Ronghui Yang
Exact Configuration for 3D Ginzburg-Landau Equation Based on Some ODEs
Author Index

The resolution of the rarefaction wave is more troublesome, because the rarefaction advances into a constant state, where the mesh is very coarse: the mesh should be refined fast enough to resolve the corner of the rarefaction correctly. Again, the AdLim strategy performs very poorly, and the CT scheme produces a step in the middle of the rarefaction. Again, ENO and S&E （not shown） are very similar to MM. On the other hand, the rarefaction wave is well resolved by the uniform grid （see also the very low values of the entropy production, which is plotted on the lower part of the figure）. Obviously, the cost of the solution with the uniform grid is much higher, since it is using a much larger number of grid points. （Note that for Sref=0.001, the rarefaction wave is correctly resolved by all schemes and allowing adaptive schemes to use cells of width 1/8192 as in the reference solution would improve dramatically the resolution of all schemes.）
Figure 3.2 shows the complete density component of the solution for the shock-acoustic wave interaction （a） together with the cell levels employed. Note that in the area behind the big shock, cells are kept to the maximum refinement level, while some coarsening is allowed in the smooth area between the small shocks on the left.On the right part of the figure （b）, we show the number of ceils used by the different adaptive algorithms as a function of time. It is clear that all algorithms use approximately the same number of ceils, and this number increases with time, as the solution evolves and more structures emerge.
In Figure 3.3 we enlarge two areas of the solution to highlight the dif- ferences among the schemes. We observe that the MM method performs quite poorly on this problem, because of the clipping of extrema by the MinMod limiter: the acoustic wave is smeared due to grid coarsening before entering into the shock and the waves do not have the correct amplitude after the shock （b）.