双曲问题（第2卷）
2012-7
高等教育出版社
李大潜，江松 主编
759
520000
This two-volume book is devoted to mathematical
theory，numerics and applications of hyperbolic problems.Hyperbolic
problems have not only a long history but alsoextremely rich
physical background.The development ishighly stimulated by their
applications to Physics，Biology，and Engineering Sciences;in
particular，by the design ofeffective numerical algorithms.Due to
recent rapiddevelopment of computers，more and more scientists
usehyperbolic partial differential equations and
relatedevolutionary equations as basic tools when proposing
newmathematical models of various phenomena and relatednumerical
algorithms.
This book contains 80 original research and review paperswhich
are written by leading researchers and promisingyoung
scientists，which cover a diverse range of multidisciplinary topics
addressing theoretical，modeling andcomputational issues arising
under the umbrella of"Hyperbolic Partial Differential Equations".It
is aimed atmathematicians，researchers in applied sciences and
graduatestudents.
Volume 2
Contributed Talks
Alin,a Chertock,Jian,-Guo Liu,Terran,ce 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 a-transformed Coordinates
Don,atella Don,atelli,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,Qian,gchang Ju,Fucai
Asymptotic Limits of the Compressible Magnetohydrodynamic
Equations
Chunhua Jin,Tong Ya'ng,Jin,gxue Yitn,
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.John,son,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 Korshun,ova,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,Martitn,Frank
Numerical Treatment of a Non-classical Transport Equation
Modelling Radiative Transfer in Atmospheric Clouds
……
Volume 1
版权页： 插图： 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）.
《双曲问题:理论、数值方法及应用(第2卷)》由高等教育出版社出版。
