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Fundamental diagrams for kinetic equations of traffic flow
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Discussion about traffic junction modelling: Conservation laws VS Hamilton-Jacobi equations
A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow
1. | Inria Sophia Antipolis-Méditerranée - EPI OPALE, 2004, Route des Lucioles - BP 93, 06902 - Sophia Antipolis Cedex, France |
2. | INRIA Sophia Antipolis - Méditerranée, EPI OPALE, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex |
References:
[1] |
B. Andreianov, P. Goatin and N. Seguin, Finite volume scheme for locally constrained conservation laws, Numer. Math., 115 (2010), 609-645.
doi: 10.1007/s00211-009-0286-7. |
[2] |
C. Bardos, A. Y. LeRoux and J. C. Nédélec, First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations, 4 (1979), 1017-1034.
doi: 10.1080/03605307908820117. |
[3] |
R. Borsche, R. M. Colombo and M. Garavello, Mixed systems: ODEs - Balance laws, Journal of Differential equations, 252 (2012), 2311-2338.
doi: 10.1016/j.jde.2011.08.051. |
[4] |
B. Boutin, C. Chalons, F. Lagoutière and P. G. LeFloch, A convergent and conservative scheme for nonclassical solutions based on kinetic relations. I, Interfaces and Free Boundaries, 10 (2008), 399-421.
doi: 10.4171/IFB/195. |
[5] |
G. Bretti and B. Piccoli, A tracking algorithm for car paths on road networks, SIAM Journal of Applied Dynamical Systems, 7 (2008), 510-531.
doi: 10.1137/070697768. |
[6] |
C. Chalons, P. Goatin and N. Seguin, General constrained conservation laws. Application to pedestrian flow modeling, Netw. Heterog. Media, 8 (2013), 433-463.
doi: 10.3934/nhm.2013.8.433. |
[7] |
R. M. Colombo and P. Goatin, A well posed conservation law with variable unilateral constraint, Journal of Differential Equations, 234 (2007), 654-675.
doi: 10.1016/j.jde.2006.10.014. |
[8] |
R. M. Colombo and A. Marson, A Hölder continuous O.D.E. related to traffic flow, The Royal Society of Edinburgh Proceedings A, 133 (2003), 759-772.
doi: 10.1017/S0308210500002663. |
[9] |
C. F. Daganzo and J. A. Laval, On the numerical treatement of moving bottlenecks, Transportation Research Part B, 39 (2005), 31-46.
doi: 10.1016/j.trb.2004.02.003. |
[10] |
C. F. Daganzo and J. A. Laval, Moving bottlenecks: A numerical method that converges in flows, Transportation Research Part B, 39 (2005), 855-863.
doi: 10.1016/j.trb.2004.10.004. |
[11] |
M. L. Delle Monache and P. Goatin, Scalar Conservation Laws with Moving Density Constraints, INRIA Research Report, n.8119, 2012. Available from: , ().
|
[12] |
Florence Giorgi, Prise en Compte des Transports en Commune de Surface dans la Mod\'elisation Macroscopique de l'Écoulement du Trafic, Ph.D thesis, Insitut National des Sciences Appliquèes de Lyon, 2002. |
[13] |
S. K. Godunov, A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Matematicheskii Sbornik, 47 (1959), 271-290. |
[14] |
N. Kružhkov, First order quasilinear equations with several independent variables, Matematicheskii Sbornik, 81 (1970), 228-255. |
[15] |
C. Lattanzio, A. Maurizi and B. Piccoli, Moving bottlenecks in car traffic flow: a pde-ode coupled model, SIAM Journal of Mathematical Analysis, 43 (2011), 50-67.
doi: 10.1137/090767224. |
[16] |
M. J. Lighthill and G. B. Whitham, On kinetic waves. II. Theory of traffic flows on long crowded roads, Proceedings of the Royal Society of London Series A, 229 (1955), 317-345.
doi: 10.1098/rspa.1955.0089. |
[17] |
P. I. Richards, Shock waves on the highways, Operational Research, 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[18] |
X. Zhong, T. Y. Hou and P. G. LeFloch, Computational Methods for propagating phase boundaries, Journal of Computational Physics, 124 (1996), 192-216.
doi: 10.1006/jcph.1996.0053. |
show all references
References:
[1] |
B. Andreianov, P. Goatin and N. Seguin, Finite volume scheme for locally constrained conservation laws, Numer. Math., 115 (2010), 609-645.
doi: 10.1007/s00211-009-0286-7. |
[2] |
C. Bardos, A. Y. LeRoux and J. C. Nédélec, First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations, 4 (1979), 1017-1034.
doi: 10.1080/03605307908820117. |
[3] |
R. Borsche, R. M. Colombo and M. Garavello, Mixed systems: ODEs - Balance laws, Journal of Differential equations, 252 (2012), 2311-2338.
doi: 10.1016/j.jde.2011.08.051. |
[4] |
B. Boutin, C. Chalons, F. Lagoutière and P. G. LeFloch, A convergent and conservative scheme for nonclassical solutions based on kinetic relations. I, Interfaces and Free Boundaries, 10 (2008), 399-421.
doi: 10.4171/IFB/195. |
[5] |
G. Bretti and B. Piccoli, A tracking algorithm for car paths on road networks, SIAM Journal of Applied Dynamical Systems, 7 (2008), 510-531.
doi: 10.1137/070697768. |
[6] |
C. Chalons, P. Goatin and N. Seguin, General constrained conservation laws. Application to pedestrian flow modeling, Netw. Heterog. Media, 8 (2013), 433-463.
doi: 10.3934/nhm.2013.8.433. |
[7] |
R. M. Colombo and P. Goatin, A well posed conservation law with variable unilateral constraint, Journal of Differential Equations, 234 (2007), 654-675.
doi: 10.1016/j.jde.2006.10.014. |
[8] |
R. M. Colombo and A. Marson, A Hölder continuous O.D.E. related to traffic flow, The Royal Society of Edinburgh Proceedings A, 133 (2003), 759-772.
doi: 10.1017/S0308210500002663. |
[9] |
C. F. Daganzo and J. A. Laval, On the numerical treatement of moving bottlenecks, Transportation Research Part B, 39 (2005), 31-46.
doi: 10.1016/j.trb.2004.02.003. |
[10] |
C. F. Daganzo and J. A. Laval, Moving bottlenecks: A numerical method that converges in flows, Transportation Research Part B, 39 (2005), 855-863.
doi: 10.1016/j.trb.2004.10.004. |
[11] |
M. L. Delle Monache and P. Goatin, Scalar Conservation Laws with Moving Density Constraints, INRIA Research Report, n.8119, 2012. Available from: , ().
|
[12] |
Florence Giorgi, Prise en Compte des Transports en Commune de Surface dans la Mod\'elisation Macroscopique de l'Écoulement du Trafic, Ph.D thesis, Insitut National des Sciences Appliquèes de Lyon, 2002. |
[13] |
S. K. Godunov, A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Matematicheskii Sbornik, 47 (1959), 271-290. |
[14] |
N. Kružhkov, First order quasilinear equations with several independent variables, Matematicheskii Sbornik, 81 (1970), 228-255. |
[15] |
C. Lattanzio, A. Maurizi and B. Piccoli, Moving bottlenecks in car traffic flow: a pde-ode coupled model, SIAM Journal of Mathematical Analysis, 43 (2011), 50-67.
doi: 10.1137/090767224. |
[16] |
M. J. Lighthill and G. B. Whitham, On kinetic waves. II. Theory of traffic flows on long crowded roads, Proceedings of the Royal Society of London Series A, 229 (1955), 317-345.
doi: 10.1098/rspa.1955.0089. |
[17] |
P. I. Richards, Shock waves on the highways, Operational Research, 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[18] |
X. Zhong, T. Y. Hou and P. G. LeFloch, Computational Methods for propagating phase boundaries, Journal of Computational Physics, 124 (1996), 192-216.
doi: 10.1006/jcph.1996.0053. |
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