diff --git a/Preface.ipynb b/Preface.ipynb
index 8e16478b..e5fe32ea 100644
--- a/Preface.ipynb
+++ b/Preface.ipynb
@@ -17,7 +17,9 @@
"\n",
"The book covers the fundamental ideas related to classical Riemann solutions, including their special structure and the types of waves that arise, as well as the ideas behind fast approximate solvers for the Riemann problem. The emphasis is on the general ideas, but each chapter delves into a particular application.\n",
"\n",
- "It is assumed that the reader has some knowledge of hyperbolic problems in advance. This book is intended to supplement rather than replace standard textbooks on the theory and numerical solution of hyperbolic PDEs. It should also be useful as a tool for students or researchers seeking to better understand the nature of Riemann solutions to a particular hyperbolic system."
+ "It is assumed that the reader has some knowledge of hyperbolic problems in advance. This book is intended to supplement rather than replace standard textbooks on the theory and numerical solution of hyperbolic PDEs. It should also be useful as a tool for students or researchers seeking to better understand the nature of Riemann solutions to a particular hyperbolic system.\n",
+ "\n",
+ "The notation generally follows that of (LeVeque 2002), but many other books cover this basic material, including for example (Hesthaven 2018), (LeVeque 1990),(Toro 2013), or (Trangenstein 2009).\n"
]
},
{
@@ -53,9 +55,8 @@
"\n",
" - On your own computer: follow the [installation instructions](https://github.com/clawpack/riemann_book/wiki/Installation) **[move these to a .md file in the repo?]**\n",
" - With Docker: follow [these instructions](https://github.com/clawpack/riemann_book/blob/master/Docker.md) to use the `Dockerfile` that is included in the [Github repository](https://github.com/clawpack/riemann_book).\n",
- " - On the [Microsoft Azure Notebooks](https://notebooks.azure.com) cloud service: Create a free account and then clone the [riemann_book library](https://notebooks.azure.com/rjleveque/libraries/riemann-book).\n",
- " - With Binder: This is still under development using the latest version of [binder](https://beta.mybinder.org/). You can try it out for these notebooks at this link: [https://mybinder.org/v2/gh/clawpack/riemann_book/master](https://mybinder.org/v2/gh/clawpack/riemann_book/master).\n",
- " This should start up a notebook server on a [Jupyterhub](https://jupyterhub.readthedocs.io/en/latest/) that lets you execute all the notebooks with no installation required."
+ " - With Binder: The cloud service [binder](https://mybinder.org/) allows you to start up a notebook server running notebooks from any Git repository (assuming it specifies the dependencies properly). You can try it out for these notebooks at this link: **Update!** [this link](https://mybinder.org/v2/gh/clawpack/riemann_book/master).\n",
+ " This should start up a notebook server on a [Jupyterhub](https://jupyterhub.readthedocs.io/en/latest/) that lets you execute all the notebooks in your browser with no local installation of the notebooks or dependencies required."
]
},
{
@@ -70,7 +71,9 @@
"\n",
"Part II introduces approximate Riemann solvers, which are an essential tool in numerical algorithms for hyperbolic PDEs. This part discusses the most important approaches to such solvers: from simple Lax-Friedrichs and HLL solvers to linearizations, including Roe solvers. Potential issues with these methods (such as the need for entropy fixes and lack of positivity) are addressed. Part II concludes with comparisons of canonical approximate solvers for the shallow water and Euler systems.\n",
"\n",
- "The remaining parts are still a work in progress at the time of this writing, and additional topics may be added at a later date. \n",
+ "The [Index](Index.ipynb) notebook contains links to the chapters of Parts I and II.\n",
+ "\n",
+ "The remaining parts are still a work in progress at the time of this writing. Some additional notebooks can be found in the [Github repository](https://github.com/clawpack/riemann_book/blob/master/Index2.ipynb) and additional topics may be added at a later date. \n",
"\n",
"Part III examines various complications that may arise when the flux function depends explicitly on the spatial coordinate. In particular, we study Riemann problems in which the flux function is also discontinuous at the same point where the initial data is discontinuous.\n",
"\n",
@@ -78,7 +81,7 @@
"\n",
"Part V focuses on non-classical problems such as non-convex conservation laws and pressureless gas.\n",
"\n",
- "Finally, in Part VI we consider some multidimensional applications."
+ "Finally, in Part VI we consider some multidimensional applications.\n"
]
}
],
diff --git a/riemann.bib b/riemann.bib
index e7daa682..6038ba24 100644
--- a/riemann.bib
+++ b/riemann.bib
@@ -182,7 +182,7 @@ @book{fvmhp
@article{osher1984,
Author = {S. Osher},
- Journal = sinum,
+ Journal = {SIAM J. Numer. Anal.},
Pages = {217--235},
Title = {{R}iemann solvers, the entropy condition, and difference approximations},
Volume = {21},
@@ -192,7 +192,7 @@ @article{osher1984
@article{delrazo2017,
Author = {M. J. del Razo and R. J. LeVeque},
- Journal = {SIAM Journal on Scientific Computing},
+ Journal = {SIAM J. Sci. Comput.},
Pages = {B486–B507},
Title = {{N}umerical methods for interface coupling of compressible and almost incompressible media},
Volume = {39(3)},
@@ -230,17 +230,6 @@ @article{Burger2008
Volume = {60},
Year = {2008}}
-@article{isaacson1992nonlinear,
- title={Nonlinear resonance in systems of conservation laws},
- author={Isaacson, Eli and Temple, Blake},
- journal={SIAM Journal on Applied Mathematics},
- volume={52},
- number={5},
- pages={1260--1278},
- year={1992},
- publisher={SIAM}
-}
-
@article{Roe1981,
title = {Approximate Riemann solvers, parameter vectors, and difference schemes},
volume = {43},
@@ -315,3 +304,26 @@ @article{roe1981approximate
pages={357--372},
year={1981},
}
+
+@book{trangenstein2009,
+ author="J. A. Trangenstein",
+ title="Numerical Solution of Hyperbolic Partial Differential Equations",
+ publisher="Cambridge University Press",
+ year="2009"
+}
+
+@book{hesthaven2018,
+ author="J. S. Hesthaven",
+ title="Numerical Methods for Conservation Laws",
+ publisher="SIAM",
+ year="2018"
+}
+
+@Book{rjl:eth,
+ author = {R. J. LeVeque},
+ title = {Numerical Methods for Conservation Laws},
+ year = {1990},
+ publisher = {Birkh{\"a}user-Verlag}
+}
+
+
diff --git a/riemann.html b/riemann.html
index a10896af..430ce21b 100644
--- a/riemann.html
+++ b/riemann.html
@@ -18,7 +18,79 @@
|
-[1]
+[1]
+ |
+
+JM Greenberg, AY Leroux, R Baraille, and A Noussair.
+ Analysis and approximation of conservation laws with source terms.
+ SIAM Journal on Numerical Analysis, 34(5):1980-2007, 1997.
+[ bib ]
+
+ |
+
+
+
+
+|
+[2]
+ |
+
+Eli Isaacson and Blake Temple.
+ Nonlinear resonance in systems of conservation laws.
+ SIAM Journal on Applied Mathematics, 52(5):1260-1278, 1992.
+[ bib ]
+
+ |
+
+
+
+
+|
+[3]
+ |
+
+Helge Holden and Nils Henrik Risebro.
+ A mathematical model of traffic flow on a network of unidirectional
+ roads.
+ SIAM Journal on Mathematical Analysis, 26(4):999-1017, 1995.
+[ bib ]
+
+ |
+
+
+
+
+|
+[4]
+ |
+
+Mauro Garavello and Benedetto Piccoli.
+ Traffic flow on networks, volume 1.
+ American institute of mathematical sciences Springfield, 2006.
+[ bib ]
+
+ |
+
+
+
+
+|
+[5]
+ |
+
+Maria Laura Delle Monache, Jack Reilly, Samitha Samaranayake, Walid Krichene,
+ Paola Goatin, and Alexandre M Bayen.
+ A pde-ode model for a junction with ramp buffer.
+ SIAM Journal on Applied Mathematics, 74(1):22-39, 2014.
+[ bib ]
+
+ |
+
+
+
+
+|
+[6]
|
Carina M Edwards, SD Howison, H Ockendon, and JR Ockendon.
@@ -32,7 +104,7 @@
|
|
-[2]
+[7]
|
Randall J LeVeque.
@@ -47,7 +119,7 @@
|
|
-[3]
+[8]
|
ADD Craik, RC Latham, MJ Fawkes, and PWF Gribbon.
@@ -61,7 +133,7 @@
|
|
-[4]
+[9]
|
EJ Watson.
@@ -75,7 +147,7 @@
|
|
-[5]
+[10]
|
Hasan Zobeyer, Nallamuthu Rajaratnam, and David Z Zhu.
@@ -89,7 +161,7 @@
|
|
-[6]
+[11]
|
S Mochon.
@@ -104,7 +176,7 @@
|
|
-[7]
+[12]
|
David I. Ketcheson and Randall J. LeVeque.
@@ -118,7 +190,7 @@
|
|
-[8]
+[13]
|
Randall J. LeVeque and Darryl H. Yong.
@@ -132,7 +204,7 @@
|
|
-[9]
+[14]
|
Randall J. LeVeque.
@@ -148,7 +220,7 @@
|
|
-[10]
+[15]
|
Michael J Lighthill and Gerald Beresford Whitham.
@@ -164,7 +236,7 @@
|
|
-[11]
+[16]
|
Paul I Richards.
@@ -178,7 +250,7 @@
|
|
-[12]
+[17]
|
Eleuterio F Toro.
@@ -193,7 +265,7 @@
|
|
-[13]
+[18]
|
R. J. LeVeque.
@@ -208,15 +280,15 @@
|
|
-[14]
+[19]
|
S. Osher.
Riemann solvers, the entropy condition, and difference
approximations.
- 21:217-235, 1984.
+ SIAM J. Numer. Anal., 21:217-235, 1984.
[ bib |
-DOI ]
+DOI ]
|
@@ -224,15 +296,15 @@
|
-[15]
+[20]
|
M. J. del Razo and R. J. LeVeque.
Numerical methods for interface coupling of compressible and almost
incompressible media.
- SIAM Journal on Scientific Computing, 39(3):B486–B507, 2017.
+ SIAM J. Sci. Comput., 39(3):B486–B507, 2017.
[ bib |
-DOI ]
+DOI ]
|
@@ -240,7 +312,7 @@
|
-[16]
+[21]
|
Mauricio J Del Razo, Yoichi Morofuji, James S Meabon, B Russell Huber, Elaine R
@@ -257,7 +329,7 @@
|
|
-[17]
+[22]
|
MJ Ivings, DM Causon, and EF Toro.
@@ -272,7 +344,7 @@
|
|
-[18]
+[23]
|
Raimund Bürger and Kenneth H. Karlsen.
@@ -287,21 +359,7 @@
|
|
-[19]
- |
-
-Eli Isaacson and Blake Temple.
- Nonlinear resonance in systems of conservation laws.
- SIAM Journal on Applied Mathematics, 52(5):1260-1278, 1992.
-[ bib ]
-
- |
-
-
-
-
-|
-[20]
+[24]
|
P. L. Roe.
@@ -317,7 +375,7 @@
|
|
-[21]
+[25]
|
Amiram Harten, Peter D Lax, and Bram van Leer.
@@ -326,6 +384,138 @@
SIAM review, 25(1):35-61, 1983.
[ bib ]
+ |
+
+
+
+
+|
+[26]
+ |
+
+Bernhard Riemann et al.
+ Über die Fortpflanzung ebener Luftwellen von endlicher
+ Schwingungsweite.
+ Verlag der Dieterichschen Buchhandlung, 1860.
+[ bib ]
+
+ |
+
+
+
+
+|
+[27]
+ |
+
+George Gabriel Stokes.
+ On a difficulty in the theory of sound.
+ The London, Edinburgh, and Dublin Philosophical Magazine and
+ Journal of Science: Series 3, 33(223):349-356, 1848.
+[ bib ]
+
+ |
+
+
+
+
+|
+[28]
+ |
+
+Constantine M Dafermos.
+ Hyperbolic conservation laws in continuum physics, volume 325 of
+ fundamental principles of mathematical sciences, 2010.
+[ bib ]
+
+ |
+
+
+
+
+|
+[29]
+ |
+
+T. Liu.
+ Hyperbolic and Viscous Conservation Laws.
+ Society for Industrial and Applied Mathematics, 2000.
+[ bib |
+DOI ]
+
+ |
+
+
+
+
+|
+[30]
+ |
+
+Sergei Konstantinovich Godunov.
+ A difference method for numerical calculation of discontinuous
+ solutions of the equations of hydrodynamics.
+ Matematicheskii Sbornik, 89(3):271-306, 1959.
+[ bib ]
+
+ |
+
+
+
+
+|
+[31]
+ |
+
+Philip L Roe.
+ Approximate riemann solvers, parameter vectors, and difference
+ schemes.
+ Journal of computational physics, 43(2):357-372, 1981.
+[ bib ]
+
+ |
+
+
+
+
+|
+[32]
+ |
+
+J. A. Trangenstein.
+ Numerical Solution of Hyperbolic Partial Differential
+ Equations.
+ Cambridge University Press, 2009.
+[ bib ]
+
+ |
+
+
+
+
+|
+[33]
+ |
+
+J. S. Hesthaven.
+ Numerical Methods for Conservation Laws.
+ SIAM, 2018.
+[ bib ]
+
+ |
+
+
+
+
+|
+[34]
+ |
+
+R. J. LeVeque.
+ Numerical Methods for Conservation Laws.
+ Birkhäuser-Verlag, 1990.
+[ bib ]
+
|
This file was generated by
diff --git a/riemann_bib.html b/riemann_bib.html
index 96d17d79..6ce2ebed 100644
--- a/riemann_bib.html
+++ b/riemann_bib.html
@@ -7,7 +7,69 @@
-riemann.bib
+riemann.bib
+@article{greenberg1997analysis,
+ title = {Analysis and approximation of conservation laws with source terms},
+ author = {Greenberg, JM and Leroux, AY and Baraille, R and Noussair, A},
+ journal = {SIAM Journal on Numerical Analysis},
+ volume = {34},
+ number = {5},
+ pages = {1980--2007},
+ year = {1997},
+ publisher = {SIAM}
+}
+
+
+
+@article{isaacson1992nonlinear,
+ title = {Nonlinear resonance in systems of conservation laws},
+ author = {Isaacson, Eli and Temple, Blake},
+ journal = {SIAM Journal on Applied Mathematics},
+ volume = {52},
+ number = {5},
+ pages = {1260--1278},
+ year = {1992},
+ publisher = {SIAM}
+}
+
+
+
+@article{holden1995mathematical,
+ title = {A mathematical model of traffic flow on a network of unidirectional roads},
+ author = {Holden, Helge and Risebro, Nils Henrik},
+ journal = {SIAM Journal on Mathematical Analysis},
+ volume = {26},
+ number = {4},
+ pages = {999--1017},
+ year = {1995},
+ publisher = {SIAM}
+}
+
+
+
+@book{garavello2006traffic,
+ title = {Traffic flow on networks},
+ author = {Garavello, Mauro and Piccoli, Benedetto},
+ volume = {1},
+ year = {2006},
+ publisher = {American institute of mathematical sciences Springfield}
+}
+
+
+
+@article{delle2014pde,
+ title = {A PDE-ODE model for a junction with ramp buffer},
+ author = {Delle Monache, Maria Laura and Reilly, Jack and Samaranayake, Samitha and Krichene, Walid and Goatin, Paola and Bayen, Alexandre M},
+ journal = {SIAM Journal on Applied Mathematics},
+ volume = {74},
+ number = {1},
+ pages = {22--39},
+ year = {2014},
+ publisher = {SIAM}
+}
+
+
+
@article{edwards2008non,
author = {Edwards, Carina M and Howison, SD and Ockendon, H and Ockendon, JR},
journal = {IMA journal of applied mathematics},
@@ -164,7 +226,7 @@ riemann.bib
@article{osher1984,
author = {S. Osher},
- journal = sinum,
+ journal = {SIAM J. Numer. Anal.},
pages = {217--235},
title = {{R}iemann solvers, the entropy condition, and difference approximations},
volume = {21},
@@ -176,7 +238,7 @@ riemann.bib
@article{delrazo2017,
author = {M. J. del Razo and R. J. LeVeque},
- journal = {SIAM Journal on Scientific Computing},
+ journal = {SIAM J. Sci. Comput.},
pages = {B486–B507},
title = {{N}umerical methods for interface coupling of compressible and almost incompressible media},
volume = {39(3)},
@@ -222,19 +284,6 @@ riemann.bib
}
-
-@article{isaacson1992nonlinear,
- title = {Nonlinear resonance in systems of conservation laws},
- author = {Isaacson, Eli and Temple, Blake},
- journal = {SIAM Journal on Applied Mathematics},
- volume = {52},
- number = {5},
- pages = {1260--1278},
- year = {1992},
- publisher = {SIAM}
-}
-
-
@article{Roe1981,
title = {Approximate Riemann solvers, parameter vectors, and difference schemes},
@@ -261,6 +310,98 @@ riemann.bib
}
+
+@book{riemann1860fortpflanzung,
+ title = {{\"U}ber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite},
+ author = {Riemann, Bernhard and others},
+ year = {1860},
+ publisher = {Verlag der Dieterichschen Buchhandlung}
+}
+
+
+
+@article{stokes1848liv,
+ title = {On a difficulty in the theory of Sound},
+ author = {Stokes, George Gabriel},
+ journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Series 3},
+ volume = {33},
+ number = {223},
+ pages = {349--356},
+ year = {1848}
+}
+
+
+
+@misc{dafermos2010hyperbolic,
+ title = {Hyperbolic conservation laws in continuum physics, volume 325 of Fundamental Principles of Mathematical Sciences},
+ author = {Dafermos, Constantine M},
+ year = {2010},
+ publisher = {Springer-Verlag, Berlin,}
+}
+
+
+
+@book{liu2000hyperbolic,
+ author = {Liu, T.},
+ title = {Hyperbolic and Viscous Conservation Laws},
+ publisher = {Society for Industrial and Applied Mathematics},
+ year = {2000},
+ doi = {10.1137/1.9780898719420}
+}
+
+
+
+@article{godunov1959difference,
+ title = {A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics},
+ author = {Godunov, Sergei Konstantinovich},
+ journal = {Matematicheskii Sbornik},
+ volume = {89},
+ number = {3},
+ pages = {271--306},
+ year = {1959},
+ publisher = {Russian Academy of Sciences, Steklov Mathematical Institute of Russian Academy of Sciences}
+}
+
+
+
+@article{roe1981approximate,
+ title = {Approximate Riemann solvers, parameter vectors, and difference schemes},
+ author = {Roe, Philip L},
+ journal = {Journal of computational physics},
+ volume = {43},
+ number = {2},
+ pages = {357--372},
+ year = {1981}
+}
+
+
+
+@book{trangenstein2009,
+ author = {J. A. Trangenstein},
+ title = {Numerical Solution of Hyperbolic Partial Differential Equations},
+ publisher = {Cambridge University Press},
+ year = {2009}
+}
+
+
+
+@book{hesthaven2018,
+ author = {J. S. Hesthaven},
+ title = {Numerical Methods for Conservation Laws},
+ publisher = {SIAM},
+ year = {2018}
+}
+
+
+
+@book{rjl:eth,
+ author = {R. J. LeVeque},
+ title = {Numerical Methods for Conservation Laws},
+ year = {1990},
+ publisher = {Birkh{\"a}user-Verlag}
+}
+
+
This file was generated by
bibtex2html 1.96.