1.
|
R. M. Colombo, M. Herty, V. Sachers,
On 2×2 Conservation Laws at a Junction,
2008,
40,
0036-1410,
605,
10.1137/070690298
|
|
2.
|
BENJAMIN BOUTIN, CHRISTOPHE CHALONS, PIERRE-ARNAUD RAVIART,
EXISTENCE RESULT FOR THE COUPLING PROBLEM OF TWO SCALAR CONSERVATION LAWS WITH RIEMANN INITIAL DATA,
2010,
20,
0218-2025,
1859,
10.1142/S0218202510004817
|
|
3.
|
Alfredo Bermúdez, Xián López, M. Elena Vázquez-Cendón,
Reprint of: Finite volume methods for multi-component Euler equations with source terms,
2018,
169,
00457930,
40,
10.1016/j.compfluid.2018.03.057
|
|
4.
|
M. Herty, J. Mohring, V. Sachers,
A new model for gas flow in pipe networks,
2010,
33,
01704214,
845,
10.1002/mma.1197
|
|
5.
|
RINALDO M. COLOMBO, PAOLA GOATIN, BENEDETTO PICCOLI,
ROAD NETWORKS WITH PHASE TRANSITIONS,
2010,
07,
0219-8916,
85,
10.1142/S0219891610002025
|
|
6.
|
Jochen Kall, Rukhsana Kausar, Stephan Trenn,
Modeling water hammers via PDEs and switched DAEs with numerical justification,
2017,
50,
24058963,
5349,
10.1016/j.ifacol.2017.08.927
|
|
7.
|
Michael Herty,
Coupling Conditions for Networked Systems of Euler Equations,
2008,
30,
1064-8275,
1596,
10.1137/070688535
|
|
8.
|
Kristen DeVault, Pierre A. Gremaud, Vera Novak, Mette S. Olufsen, Guillaume Vernières, Peng Zhao,
Blood Flow in the Circle of Willis: Modeling and Calibration,
2008,
7,
1540-3459,
888,
10.1137/07070231X
|
|
9.
|
CIRO D'APICE, BENEDETTO PICCOLI,
VERTEX FLOW MODELS FOR VEHICULAR TRAFFIC ON NETWORKS,
2008,
18,
0218-2025,
1299,
10.1142/S0218202508003042
|
|
10.
|
Stephan Gerster, Michael Herty, Michael Chertkov, Marc Vuffray, Anatoly Zlotnik,
2019,
Chapter 8,
978-3-030-27549-5,
59,
10.1007/978-3-030-27550-1_8
|
|
11.
|
Martin Gugat, Michael Herty, Axel Klar, Günther Leugering, Veronika Schleper,
2012,
Chapter 7,
978-3-0348-0132-4,
123,
10.1007/978-3-0348-0133-1_7
|
|
12.
|
Mapundi K. Banda, Michael Herty, Jean-Medard T. Ngnotchouye,
Toward a Mathematical Analysis for Drift-Flux Multiphase Flow Models in Networks,
2010,
31,
1064-8275,
4633,
10.1137/080722138
|
|
13.
|
Jeroen J. Stolwijk, Volker Mehrmann,
Error Analysis and Model Adaptivity for Flows in Gas Networks,
2018,
26,
1844-0835,
231,
10.2478/auom-2018-0027
|
|
14.
|
Mapundi K. Banda, Axel-Stefan Häck, Michael Herty,
Numerical Discretization of Coupling Conditions by High-Order Schemes,
2016,
69,
0885-7474,
122,
10.1007/s10915-016-0185-x
|
|
15.
|
Evgenii S. Baranovskii, Vyacheslav V. Provotorov, Mikhail A. Artemov, Alexey P. Zhabko,
Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results,
2021,
13,
2073-8994,
1300,
10.3390/sym13071300
|
|
16.
|
Rinaldo M. Colombo, Mauro Garavello,
On the Cauchy Problem for the p-System at a Junction,
2008,
39,
0036-1410,
1456,
10.1137/060665841
|
|
17.
|
J.B. Collins, P.A. Gremaud,
Analysis of a domain decomposition method for linear transport problems on networks,
2016,
109,
01689274,
61,
10.1016/j.apnum.2016.06.004
|
|
18.
|
Alfredo Bermúdez, Xián López, M. Elena Vázquez-Cendón,
Treating network junctions in finite volume solution of transient gas flow models,
2017,
344,
00219991,
187,
10.1016/j.jcp.2017.04.066
|
|
19.
|
Martin Gugat, Michael Herty, Siegfried Müller,
Coupling conditions for the transition from supersonic to subsonic fluid states,
2017,
12,
1556-181X,
371,
10.3934/nhm.2017016
|
|
20.
|
H. Egger,
A Robust Conservative Mixed Finite Element Method for Isentropic Compressible Flow on Pipe Networks,
2018,
40,
1064-8275,
A108,
10.1137/16M1094373
|
|
21.
|
Yannick Holle,
Kinetic relaxation to entropy based coupling conditions for isentropic flow on networks,
2020,
269,
00220396,
1192,
10.1016/j.jde.2020.01.005
|
|
22.
|
Mohamed Elshobaki, Alessandro Valiani, Valerio Caleffi,
Numerical modelling of open channel junctions using the Riemann problem approach,
2019,
57,
0022-1686,
662,
10.1080/00221686.2018.1534283
|
|
23.
|
Mapundi K. Banda, Michael Herty,
Towards a space mapping approach to dynamic compressor optimization of gas networks,
2011,
32,
01432087,
253,
10.1002/oca.929
|
|
24.
|
Rinaldo M. Colombo,
2011,
Chapter 13,
978-1-4419-9553-7,
267,
10.1007/978-1-4419-9554-4_13
|
|
25.
|
Seok Woo Hong, Chongam Kim,
A new finite volume method on junction coupling and boundary treatment for flow network system analyses,
2011,
65,
02712091,
707,
10.1002/fld.2212
|
|
26.
|
Michael Herty, Mohammed Seaïd,
Assessment of coupling conditions in water way intersections,
2013,
71,
02712091,
1438,
10.1002/fld.3719
|
|
27.
|
Gunhild A. Reigstad,
Existence and Uniqueness of Solutions to the Generalized Riemann Problem for Isentropic Flow,
2015,
75,
0036-1399,
679,
10.1137/140962759
|
|
28.
|
R. Borsche, A. Klar,
Flooding in urban drainage systems: coupling hyperbolic conservation laws for sewer systems and surface flow,
2014,
76,
02712091,
789,
10.1002/fld.3957
|
|
29.
|
Pascal Mindt, Jens Lang, Pia Domschke,
Entropy-Preserving Coupling of Hierarchical Gas Models,
2019,
51,
0036-1410,
4754,
10.1137/19M1240034
|
|
30.
|
Alexandre Morin, Gunhild A. Reigstad,
Pipe Networks: Coupling Constants in a Junction for the Isentropic Euler Equations,
2015,
64,
18766102,
140,
10.1016/j.egypro.2015.01.017
|
|
31.
|
Mapundi Kondwani Banda,
2015,
Chapter 9,
978-3-319-11321-0,
439,
10.1007/978-3-319-11322-7_9
|
|
32.
|
Yogiraj Mantri, Sebastian Noelle,
Well-balanced discontinuous Galerkin scheme for 2 × 2 hyperbolic balance law,
2021,
429,
00219991,
110011,
10.1016/j.jcp.2020.110011
|
|
33.
|
Mauro Garavello, Benedetto Piccoli,
Conservation laws on complex networks,
2009,
26,
0294-1449,
1925,
10.1016/j.anihpc.2009.04.001
|
|
34.
|
Mauro Garavello,
2011,
Chapter 15,
978-1-4419-9553-7,
293,
10.1007/978-1-4419-9554-4_15
|
|
35.
|
Andrea Corli, Ingenuin Gasser, Mária Lukáčová-Medvid’ová, Arne Roggensack, Ulf Teschke,
A multiscale approach to liquid flows in pipes I: The single pipe,
2012,
219,
00963003,
856,
10.1016/j.amc.2012.06.054
|
|
36.
|
Raul Borsche, Jochen Kall,
ADER schemes and high order coupling on networks of hyperbolic conservation laws,
2014,
273,
00219991,
658,
10.1016/j.jcp.2014.05.042
|
|
37.
|
Mapundi K. Banda, Michael Herty,
Multiscale modeling for gas flow in pipe networks,
2008,
31,
01704214,
915,
10.1002/mma.948
|
|
38.
|
Gunhild A. Reigstad, Tore Flåtten, Nils Erland Haugen, Tor Ytrehus,
Coupling constants and the generalized Riemann problem for isothermal junction flow,
2015,
12,
0219-8916,
37,
10.1142/S0219891615500022
|
|
39.
|
Alfredo Bermúdez, Xián López, M. Elena Vázquez-Cendón,
Finite volume methods for multi-component Euler equations with source terms,
2017,
156,
00457930,
113,
10.1016/j.compfluid.2017.07.004
|
|
40.
|
Raul Borsche,
Numerical schemes for networks of hyperbolic conservation laws,
2016,
108,
01689274,
157,
10.1016/j.apnum.2016.01.006
|
|
41.
|
Alexandre Bayen, Maria Laura Delle Monache, Mauro Garavello, Paola Goatin, Benedetto Piccoli,
2022,
Chapter 3,
978-3-030-93014-1,
39,
10.1007/978-3-030-93015-8_3
|
|
42.
|
Christian Contarino, Eleuterio F. Toro, Gino I. Montecinos, Raul Borsche, Jochen Kall,
Junction-Generalized Riemann Problem for stiff hyperbolic balance laws in networks: An implicit solver and ADER schemes,
2016,
315,
00219991,
409,
10.1016/j.jcp.2016.03.049
|
|
43.
|
Michael Herty, Nouh Izem, Mohammed Seaid,
Fast and accurate simulations of shallow water equations in large networks,
2019,
78,
08981221,
2107,
10.1016/j.camwa.2019.03.049
|
|
44.
|
F. Daude, P. Galon,
A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction,
2018,
362,
00219991,
375,
10.1016/j.jcp.2018.01.055
|
|
45.
|
Benedetto Piccoli, Andrea Tosin,
2013,
Chapter 576-3,
978-3-642-27737-5,
1,
10.1007/978-3-642-27737-5_576-3
|
|
46.
|
Gunhild Allard Reigstad, Tore Flåtten,
2015,
Chapter 66,
978-3-319-10704-2,
667,
10.1007/978-3-319-10705-9_66
|
|
47.
|
F. Daude, R.A. Berry, P. Galon,
A Finite-Volume method for compressible non-equilibrium two-phase flows in networks of elastic pipelines using the Baer–Nunziato model,
2019,
354,
00457825,
820,
10.1016/j.cma.2019.06.010
|
|
48.
|
Benedetto Piccoli, Andrea Tosin,
2012,
Chapter 112,
978-1-4614-1805-4,
1748,
10.1007/978-1-4614-1806-1_112
|
|
49.
|
Mouhamadou Samsidy Goudiaby, Gunilla Kreiss,
Existence result for the coupling of shallow water and Borda–Carnot equations with Riemann data,
2020,
17,
0219-8916,
185,
10.1142/S021989162050006X
|
|
50.
|
Michael Herty, Mohammed Seaïd,
Simulation of transient gas flow at pipe-to-pipe intersections,
2008,
56,
02712091,
485,
10.1002/fld.1531
|
|
51.
|
RINALDO M. COLOMBO, CRISTINA MAURI,
EULER SYSTEM FOR COMPRESSIBLE FLUIDS AT A JUNCTION,
2008,
05,
0219-8916,
547,
10.1142/S0219891608001593
|
|
52.
|
Mapundi K. Banda, Michael Herty, Jean Medard T. Ngnotchouye,
On linearized coupling conditions for a class of isentropic multiphase drift-flux models at pipe-to-pipe intersections,
2015,
276,
03770427,
81,
10.1016/j.cam.2014.08.021
|
|
53.
|
Christophe Chalons, Pierre-Arnaud Raviart, Nicolas Seguin,
The interface coupling of the gas dynamics equations,
2008,
66,
0033-569X,
659,
10.1090/S0033-569X-08-01087-X
|
|
54.
|
Sara Grundel, Michael Herty,
Hyperbolic discretization of simplified Euler equation via Riemann invariants,
2022,
106,
0307904X,
60,
10.1016/j.apm.2022.01.006
|
|
55.
|
Zlatinka Dimitrova,
Flows of Substances in Networks and Network Channels: Selected Results and Applications,
2022,
24,
1099-4300,
1485,
10.3390/e24101485
|
|
56.
|
Edwige Godlewski, Pierre-Arnaud Raviart,
2021,
Chapter 7,
978-1-0716-1342-9,
627,
10.1007/978-1-0716-1344-3_7
|
|
57.
|
Jens Brouwer, Ingenuin Gasser, Michael Herty,
Gas Pipeline Models Revisited: Model Hierarchies, Nonisothermal Models, and Simulations of Networks,
2011,
9,
1540-3459,
601,
10.1137/100813580
|
|
58.
|
Raul Borsche, Jochen Kall,
High order numerical methods for networks of hyperbolic conservation laws coupled with ODEs and lumped parameter models,
2016,
327,
00219991,
678,
10.1016/j.jcp.2016.10.003
|
|
59.
|
MOUHAMADOU SAMSIDY GOUDIABY, GUNILLA KREISS,
A RIEMANN PROBLEM AT A JUNCTION OF OPEN CANALS,
2013,
10,
0219-8916,
431,
10.1142/S021989161350015X
|
|
60.
|
Martin Gugat, Michael Herty,
2022,
23,
9780323850599,
59,
10.1016/bs.hna.2021.12.002
|
|
61.
|
Benedetto Piccoli, Andrea Tosin,
2009,
Chapter 576,
978-0-387-75888-6,
9727,
10.1007/978-0-387-30440-3_576
|
|
62.
|
Gunhild A. Reigstad,
Numerical network models and entropy principles for isothermal junction flow,
2014,
9,
1556-181X,
65,
10.3934/nhm.2014.9.65
|
|
63.
|
Andrea Corli, Massimiliano D. Rosini, Ulrich Razafison,
2024,
Mathematical Modeling of Chattering and the Optimal Design of a Valve*,
979-8-3503-1633-9,
76,
10.1109/CDC56724.2024.10886245
|
|
64.
|
Michael T. Redle, Michael Herty,
An asymptotic-preserving scheme for isentropic flow in pipe networks,
2025,
20,
1556-1801,
254,
10.3934/nhm.2025013
|
|