Liste of Publications

PAPERS

63. C. Berthon, L. Martaud                   (pdf file)  
    Local fully discrete entropy stability for a genuine second-order scheme for scalar hyperbolic equations
    Journal of Numerical Mathematics, to appear
    

62. C. Berthon, M. Castro Diaz, L. Martaud, T. Morales de Luna                   (pdf file)  
    How to make fully discrete entropy stability of three-point well-balanced finite-volume schemes
    Journal of Numerical Mathematics, to appear
    

61. C. Berthon, B. Braconnier, G. L. Dongmo Nguepi, C. Preux, Q. H. Tran                   (pdf file)  
    Towards weakly hyperbolic models for inaccessible pore volume model in polymer flooding
    Mathematical Methods in the Applied Sciences, to appear
    

60. C. Berthon, V. Michel-Dansac, A. Thomann                   (pdf file)  
    An entropy-stable and fully well-balanced scheme for the Euler equations with gravity
    Math. of Comp., 95(359), pp. 1251-1292 (2026)
    

59. L. Martaud, C. Berthon                   (pdf file)  
    (Fully) well-balanced entropy stable Godunov numerical schemes for the shallow water equations
    M2AN, to appear
    

58. C. Berthon, B. Braconnier, G. L. Dongmo Nguepi, C. Preux, Q. H. Tran                   (pdf file)  
    A relaxation scheme for the simulation of two-phase flows with inaccessible pore volume in polymer flooding
    Internat. J. Numer. Methods Fluids, 97(3), 244-266 (2025)
    

57. C. Berthon, V. Michel-Dansac                   (pdf file)  
    A fully well-balanced hydrodynamic reconstruction
    Journal of Numerical Mathematics, 32(3), pp. 275-299 (2024)
    

56. C. Berthon, M. J. Castro Diaz, A. Duran, T. Morales de Luna, K.Saleh                  (pdf file)  
    Artificial viscosity to get both robustness and discrete entropy inequalities
    J. Sci. comput., 97(3), 65 (2023)
    

55. S. Bulteau, C. Berthon, M. Bessemoulin-Chatard                      (pdf file)
    An Asymptotic Preserving scheme for the shallow- water equations with Manning friction using viscous correction of the HLL scheme
    Numer. Methods Partial Diff. Equations, 39(5), pp. 3919-3941 (2023).

54. M. Badsi, C. Berthon, L. Martaud                      (pdf file)
    A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws
    SMAI J. of Comput. Math., 9, pp. 31-60 (2023).

53. C. Berthon, S. Bulteau, F. Foucher, M. M'Baye, V. Michel-Dansac                      (pdf file)
    Very easy high-order well-balanced reconstruction for hyperbolic systems with source terms
    SIAM J. Sci. Comput., 4(4), pp. A2506-A2535 (2022).

52. V. Michel-Dansac, C. Berthon, S. Clain, F. Foucher                      (pdf file)
    A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction
    Computer and Fluids, 230, 105152 (2021).

51. S. Bulteau, M. Badsi, C. Berthon, M. Bessemoulin-Chatard                      (pdf file)
    A fully well-balanced and asymptotic preserving scheme for the shallow-water equations with a generalized Manning friction source term
    Calcolo, 58(4), 41 (2021).

50. C. Berthon, M. M'Baye, M. H. Le, D. Seck                    (pdf file)
    A well-defined moving steady states capturing Godunov-type scheme for Shallow-water model
    Int. J. Finite Volumes, 15 (2020).

49. M. Badsi, C. Berthon, A. Crestteto                      (pdf file)
    A stable fixed point method for the numerical simulation of a kinetic collisional sheath
    J. Comput. Phys., 429, 109990 (2020).

48. K. Laurent, E. Flauraud, C. Preux, Q. H. Tran, C. Berthon                (pdf file)
    Design of coupled finite volume schemes minimizing the grid orientation effect in reservoir simulation
    J. Comput. Phys., 425, 109923 (2020).

47. B. Ghitti, C. Berthon, M. H. Le, E. F. Toro                (pdf file)
    A fully well-balanced scheme for the 1D blood flow equations with friction source term
    J. Comput. Phys., 421, 109750 (2020).

46. C. Berthon, C. Klingenberg, M. Zenk                 (pdf file)
    An all Mach number relaxation upwind scheme
    SMAI J. of Comput. Math., 6 (2020) pp. 1-31

45. C. Berthon, M. Bessemoulin-Chatard, A. Crestetto, F. Foucher                 (pdf file)
    A Riemann solution approximation based on the zero diffusion-dispersion limit of Dafermos reformulation type problem
    Calcolo, 56 (2019), pp. 1-32 pp.

44. C. Berthon, A. Duran, F. Foucher, K. Saleh, J. de D. Zabsonré                 (pdf file)
    Improvement of the hydrostatic reconstruction scheme to get fully discrete entropy inequalities
    J. Sci. Comput., 80 (2019), pp. 924-956

43. S. Bulteau, C. Berthon, M. Bessemoulin-Chatard                  (pdf file)
    Convergence rate of an asymptotic preserving scheme for the diffusive limit of the p-system with damping
    Comm. Math. Sci., 17 (2019), pp. 1459-1486

42. B. Braconnier, C. Preux, E. Flauraud, Q.-H. Tran, C. Berthon
    An analysis of physical models and numerical schemes for polymer flooding simulations
    Computational Geosciences, 21 (2017), pp. 1267-1279
    

41. V. Michel-Dansac, C. Berthon, S. Clain, F. Foucher                (pdf file)
    A well-balanced scheme for the shallow-water equations with topography or Manning friction
    J. Comput. Phys., 335 (2017), pp. 115-154

40. C. Berthon, M. Bessemoulin-Chatard, H. Mathis                  (pdf file)
    Numerical convergence rate for a diffusive limit of hyperbolic systems : p-system with damping
    SMAI J. of Comput. Math.,  2 (2016), p. 99-119
    

39. V. Michel-Dansac, C. Berthon, S. Clain, F. Foucher                 (pdf file)
    A well-balanced scheme for the shallow-water equations with topography
    Comput. Math. Appl., 72 (2016), pp. 568-593
    

38. C. Berthon, G. Moebs. C. Sarazin-Desbois, R.Turpault               (pdf file)
    An asymptotic-preserving scheme for systems of conservation laws with source terms on 2D unstructured meshes
    Comm. in Appl. Math. and Comput. Sci., 11 (2016), pp. 55-77
    

37. V. Desveaux, M. Zenk, C. Berthon, C. Klingenberg                (pdf file)
    A well-balanced scheme to capture non-explicit steady states in the Euler equations with gravity
    Internat. J. Numer. Methods Fluids, 81 (2016), pp. 104-127

36. C. Berthon, A. Crestetto, F. Foucher,                      (pdf file)
    A well-balanced finite volume scheme for a mixed hyperbolic/parabolic system to model chemotaxis,
    J. Sci. Comput., 67 (2016), pp. 618-643
    

35. V. Desveaux, M. Zenk, C. Berthon, C. Klingenberg                (pdf file)
    Well-balanced schemes to capture non-explicit steady states : RIPA model
    Math. of Comput., 85 (2016), pp. 1571-1602

34. C. Berthon, C. Chalons                                   (pdf file)
    A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations
    Math. of Comput., 85 (2016), pp. 1281-1307
    

33. A. Duran, F. Marche, R.Turpault, C. Berthon                    (pdf file)
    Asymptotic preserving scheme for the shallow water equations with source terms on unstructured meshes
    J. Comput. Phys., 287 (2015), pp. 184-206
    

32. C. Berthon, B. Dubroca, A. Sangam                              (pdf file)
    An entropy preserving relaxation scheme for the Ten-Moments equations with source terms
    Comm. Math. Sci., 13 (2015), pp. 2119-2154
    

31. C. Berthon, F. Foucher, T. Morales                        (pdf file)
    An efficient splitting technique for two-layer Shallow-Water model
    Numer. Methods Partial Diff. Equations, 31 (2015), pp. 1396-1423
    

30. C. Berthon, B. Boutin, R. Turpault                          (pdf file)
    Shock profiles for the Shallow-water Exne model
    Adv. Appl. Math. Mech., 7 (2015), pp. 267-294
    

29. C. Berthon, V. Desveaux                                         (pdf file)
    An entropy preserving MOOD scheme for the Euler equations,
    Int. J. Finite Volumes, 11 (2014), pp. 1-39
    
    

28. C. Berthon, Y. Coudière, V. Desveaux                             (pdf file)
    Second-order MUSCL schemes based on dual mesh gradient reconstruction (DMGR),
    Math. Model. Numer. Anal., 48 (2014), pp. 583-602

27. J. Vides, B. Braconnier, A. Audit, C. Berthon, B. Nkonga              (pdf file)
    A Godunov-type solver for the numerical approximation of gravitational flows
    Comm. Comput. Physics, 15 (2014), pp. 46-75

26. K. Krycki, C. Berthon, M. Frank, R. Turpault                             (pdf file)
    Asymptotic preserving numerical schemes for a nonclassical radiation transport model for atmospheric clouds
    Math. Meth. Applied Scie., 36 (2013), pp. 2101-2116
    

25. C. Berthon, C. Sarazin, R. Turpault                             (pdf file)
    Space-time Generalized Riemann Problem solvers of order $k$ for linear advection with unrestricted time step
    J. Sci. Comput., 55 (2013), pp. 268-308
    

24. C. Berthon, C. Chalons, R. Turpault                             (pdf file)
    Asymptotic-preserving Godunov-type numerical schemes for hyperbolic systems with stiff and non-stiff relaxation terms
    Num. Method Partial Diff. Equations, 29 (2013), pp. 1149-1172
    

23. C. Berthon, F. Foucher,                                                 (pdf file)
    Efficient wellbalanced hydrostatic upwind schemes for shallowwater equations
    J. Comput. Phys., 231 (2012), pp. 4993-5015

22. C. Berthon, B. Dubroca, A. Sangam                              (pdf file)
    A local entropy minimum principle for deriving entropy preserving schemes
    SIAM Numer. Anal., 50 (2012), pp. 468-491

21. C. Berthon, P. G. LeFloch, R. Turpault                           (pdf file)
    Late-time relaxation limits of nonlinear hyperbolic systems. A general framework
    Math. of Comput., 82 (2013), pp. 831-860

20. C. Berthon, F. Coquel, P. G. LeFloch                                 (pdf file)
    Why many theories of shock waves are necessary : Kinetic relations for nonconservative systems
    Proc. Royal Soc. Edinburgh, 142 (2012), pp. 1-37
    

19. C. Berthon, F. Marche, R. Turpault                                  (pdf file)
    An efficient scheme on wet/dry transitions for Shallow Water Equations with friction
    Computer and Fluids, 48 (2011), pp. 192-201
    
    

18. C. Berthon, M. Frank, C. Sarazin, R. Turpault                   (pdf file)
    Numerical methods for balance laws with space dependent flux : application to radiotherapy dose calculation
    Comm. Comput. Physics, 10 (2011), pp. 1184-1210

17. C. Berthon, R. Turpault                                                      (pdf file)
    Asymptotic preserving schemes
    Num. Method Partial Diff. Equations, 27, No. 6, pp. 1396-1422 (2011)

16. C. Berthon, J. Dubois, B. Dubroca, T.-H. Nguyen-Bui, R. Turpault  (pdf file)
    A Free Streaming Contact Preserving Scheme for the M1 Model
    Adv. Appl. Math. Mech., 3 (2010), pp. 259-285

15. C. Berthon, F. Marche                                                      (pdf file)
    A positive preserving hight order VFRoe scheme for shallow water equations: A class of relaxation schemes
    SIAM J. Scie. Comput, 30, No 5, pp. 2587-2612 (2008)

14. C. Berthon, F. Coquel                                                      (pdf file)
    Shock layers for turbulence models
    M3AS, 18, No 8, pp. 1443-1479 (2008)

13. C. Berthon, P. Charrier, B. Dubroca                                (pdf file)
    An HLLC scheme to solve the M₁ model of radiative transfer in two space dimensions
    J. Sci. Comput., 31. no. 3, pp. 347-389 (2007)

12. C. Berthon, B. Nkonga                                                    (pdf file)
    Multifluid numerical approximations based on multipressure formulation
    Comp. Fluids, 36, No 2, pp. 467-479 (2007)

11. C. Berthon, F. Coquel                                                      (pdf file)
    Nonlinear projection methods for multi-entropies Navier-Stokes systems
    Math. Comput., 76, pp. 1163-1194 (2007) 

10. C. Berthon                                                                        (pdf file)
    Numerical approximations of the 10-moment Gaussian closure
    Math. Comput., 75, pp. 1809-1831 (2006)

9. C. Berthon                                                                        (pdf file)
   Robustness of MUSCL schemes for 2D unstructured meshes
   J. Comp. Physics, 218,  pp. 495-509 (2006)

8. C. Berthon                                                                        (pdf file)
   Why the MUSCL-Hancock scheme is L¹-stable
   Numer. Math., 104, pp. 27-46 (2006)
   

7. C. Berthon, M. Breuss, M.-O. Titeux                               (pdf file)
   A relaxation scheme for pressureless gas dynamics
   Num. Method Partial Diff. Equations, 22, pp. 484-505 (2006)
   

6. C. Berthon, F. Coquel                                                       (pdf file)
   Multiple solutions for compressible turbulent flow models
   Comm. Math. Sciences, 4, pp. 497-511 (2006)
   

5. C. Berthon                                                                         (pdf file)
   Stability of the MUSCL schemes for the Euler equations
   Comm. Math. Sciences, 3, pp. 133-158 (2005)
   

4. C. Berthon, B. Nkonga                                                      (pdf file)
   Numerical model  of a compressible multi-fluid fluctuating flow
   Inter. J. finite volumes, Volume 2, No 2 (2005)
   

3. M. Baudin, C. Berthon, F. Coquel, R. Masson, Q. H. Tran               (pdf file)
   A relaxation method for two-phase flow models with hydrodynamic closure law
   Numer. Math., 99, No. 3, pp. 411--440  (2005)

2. C. Berthon, D. Reignier                                                     (pdf file)
   A combustion model and approximate nonlinear projection scheme
   M2AN, Volume 37, No 3, pp. 451-478 (2003)

1. C. Berthon, F. Coquel, J.M. Hérard, M. Uhlmann             (pdf file)
   An approximate solution of the Riemann problem for a realisable second-moment turbulent closure
   Shock Waves, Springer Verlag editor,Volume 11, Issue 4, pp. 245-269 (2002)

SHORT COMMUNICATIONS

5. C. Berthon, V. Michel-Dansac
   A simple fully well-balanced and entropy preserving scheme for the shallow-water equations
   Applied Mathematics Letters, 86 (2018), pp.284-290

4. C. Berthon, S. Cordier, M. H. Le, O. Delestre
   An analytical solution of Shallow Water system coupled to Exner equation
   C. R. Acad. Sci. Paris, Ser. I, 350, pp. 183-186 (2012)

3. C. Berthon, P. Charrier, B. Dubroca
   An asymptotic preserving relaxation scheme for a moment model of radiative transfer
   C. R. Acad. Sci. Paris, Ser. I, 344, pp. 467-472 (2007)

2. C. Berthon
   Inégalités d'entropie pour un schéma de relaxation
   C. R., Math., Acad. Sci. Paris 340, No.1, 63-68 (2005)
   

1. C. Berthon
   Schéma nonlinéaire pour l'aproximation numérique d'un système hyperbolique non conservatif
   C. R. Acad. Sci. Paris, Ser. I, 335, pp. 1069-1072 (2002)

1. C. Berthon, A. Duran, S. Khaled                 (pdf file)
   An easy control of the artificial numerical viscosity to get discrete entropy inequalities when approximating hyperbolic systems of conservation laws
   Continuum Mechanics, Applied Mathematics and Scientific Computing : Godunov's Legacy
   Springer Nature Switzerland AG (2020)
   

2. R. Abgrall, D. Aregba, C. Berthon, M. Castro, C. Parés
   Special issue : Numerical approximations of hyperbolic systems with source terms and applications
   J. Sci. Comput. 48 (2011)
   

3. T. Goudon, J.- E. Morel, B. Després, C. Buet, C. Berthon, J. Dubois, R. Turpault, J.-F. Coulombel
   Mathematical Models and Numerical Methods for Radiative Transfer
   Panoramas et synthèses, fascicule 28 (2009)

PROCEEDINGS

33. L. Martaud, C. Berthon
    Entropy stable Godunov numerical schemes for the Euler equations
    Harmonic Analysis and Partial Differential Equations - Proceedings of the Workshop in Abidjan, Cote d'Ivoire
    May 22-26, 2023, pulished in the book series Applied and Numerical Harmonic Analysis
    

32. L. Martaud, C. Berthon
    The existence of well-balanced entropy stable numerical scheme for the Ripa model with the topography source term
    XVII CMA/XXVII CEDYA, p. 89 (2022)

31. G. Dongmo , B. Braconnier, C. Preux, Q.-H. Tran, C. Berthon
    Glimm and finite volume schemes for polymer flooding model with and without inaccessible pore volume law
    ECMOR XVII, vol. 2020, pp. 1-21 (2020)

30. G. Dongmo Nguep, B. Braconnier, C. Preux, Q.-H. Tran, C. Berthon
    A relaxation method for the simulation of possibly non-hyperbolic polymer flooding models with inaccessible pore volume effect
    Finite Volumes for complex Application IX, Springer International Publishing, pp. 445-453 (2020)

29. K. Laurent, E. Flauraud, C. Preux, Q.-H. Tran, C. Berthon
    Design of coupled finite volume schemes minimizing the grid orientation effect in reservoir simulation
    Finite Volumes for complex Application IX, Springer International Publishing, pp. 575-583 (2020)
    

28. C. Berthon, R. Loubère, V. Michel-Dansac
    A second-order well-balanced scheme for the shallow-water equations with topography
    Hyperbolic problems : Theory, Numerics, Applications (Aachen 2016), Springer, pp. 165-177
    

27. B. Braconnier, C. Preux, E. Flauraud, Q. Huy Tran, C. Berthon
    An Analysis of Physical Models and Numerical Schemes for Polymer Flooding Simulations
    ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery.
    

26. C. Berthon, C. Chalons, S. Cornet, G. Sperone
    Fully well-balanced, positive and simple approximate Riemann solver for shallow water equations
    Hyperbolic problems : Theory, Numerics, Applications (Rio 2014),
    Bull. Braz. Math. Soc., New Series, 47, pp. 117-130 (2016)

25. A. Duran, F. Marche, C. Berthon, R. Turpault
    Numerical discretizations for shallow water equations with source terms on unstructured meshes
    Hyperbolic problems : Theory, Numerics, Applications (Padou 2012)
    AIMS Series on Applied Mathematics, Volume 8, pp. 541-549 (2014)
    

24. R. Turpault, C. Berthon, B. Boutin
    Profils de choc pour St-Venant-Exner
    Actes du colloque Edp-Normandie, Caen 2013, pp. 115-124 (2014)
    

23. C. Berthon, M. De Leffe, V. Michel-Dansac
    A conservative well-balanced hybrid SPH scheme for the shallow-water model
    Finite Volumes for complex Application VII, Springer, pp. 817-825 (2014)
    

22. C. Berthon, G. Moebs, R. Turpault
    An asymptotic-preserving scheme for systems of conservation laws with source terms on 2D unstructured meshes
    Finite Volumes for complex Application VII, Springer, pp. 107-115 (2014)
    

21. V. Desveaux, M. Zenk, C. Berthon, C. Klingenberg
     well-balanced scheme for the Euler equation with a gravitational potential
    Finite Volumes for complex Application VII, Springer, pp. 217-226-115 (2014)
    

20. F. McKee, C. Preux, C. Berthon
    Relative Permeability Homogenization by a Regression Technique
    75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013

19. F. McKee, C. Preux, C. Berthon
    Homogenization of Relative Permeabilities Curves for Twophase Flow in Porous Media Using an Optimization Method
    13th European Conference on the Mathematics of Oil Recovery (2012)

18. F. McKee, C. Preux, C. Berthon
    Upscaling of Two-phase Flows for Heterogeneous Porous Media by an Optimization Approach
    Flow and mechanics in natural porous media from pore to field scale
    Pore2Field, IFP Energies nouvelles, France (2011)

17. C. Berthon, F. Foucher                                 (pdf file)
    Hydrostatic upwind schemes for shallow-water equations,
    Finite Volumes for Complex Application VI, Springer Proceedings in Mathematics 4 (2011), pp. 97-106
    

16. C. Berthon, R. Turpault
    Finite Volumes Asymptotic Preserving Schemes for Systems of Conservation Laws with Stiff Source Terms
    Finite Volumes for Complex Application VI, Springer Proceedings in Mathematics 4 (2011), pp. 107-116
    

15. C. Berthon, Y. Coudière, V. Desveaux
    Developement of DDFV methods for the Euler equations
    Finite Volumes for Complex Application VI, Springer Proceedings in Mathematics 4 (2011), pp. 117-124
    

14. C. Berthon, C. Sarazin, R. Turpault
    Numerical approximations of asymptotic regimes
    Proceedings of the 3rd International Workshop on Radiation of High Temperature Gases in Atmospheric Entry, 689 (2011), pp.17

13. C. Berthon, R. Turpault
    A numerical correction of the M1-model in the diffusive limit
    Discrete Contin. Dyn. Syst. Ser. B, 5, 245-255 (2012).
    

12. C. Berthon, F. Marche
    A positive well-balanced VFRoe-ncv scheme for non-homogeneous shallow-water equations
    ISCM-EPMESC proceedings, AIP Conference Proceedings 1233, pp. 1495-1500 (2010)

11. F. Marche, C. Berthon
    A robust high order VFRoe scheme for shallow-water equations
    Proceedings of Symposia in Applied Mathematics, 62, pages 785-794 (2009)

10. C. Berthon
    Robustness of the MUSCL-schemes
    Progress in Industrial Mathematics at ECMI 2006,
    Mathematics in Industry,12 Springer, pages 933-938 (2009)
    

9. C. Berthon
   A stable gradient reconstruction for the MUSCL schemes applied to systems of conservation laws
   Special Issue: Numerical Simulation of Complex and Multiphase Flows (Ed. P. Helluy)
   Flow, Turbulence and Combustion, 76, pages 343-351 (2006)

8. C. Berthon, B. Braconnier, J. Claudel, B. Nkonga
   A relaxation method for a two phase flow with surface tension.
   Numerical mathematics and advanced applications,
   ENUMATH 2005, Springer, pages 843-851 (2006)

7. C. Berthon, B. Braconnier, B. Nkonga
   Numerical approximation of a degenerated non-conservative multifluid model: relaxation scheme
   Inter. J. Num. Methods in Fluids, 48, Issue 1, pages 85-90 (2005)

6. C. Berthon
   A relaxation scheme to approximate the 10-moment Gaussian closure
   European Conference on Computational Fluid dynamics, ECCOMAS CFD 2006
   P. Wesseling, E. Onate and J. Periaux (Eds)

5. C. Berthon, D. Reignier
   Nonlinear projection methods to approximate combustion turbulent flows,
   Comput. Fluids, 33, No.5-6, pages 679-685 (2004)

4. C. Berthon, B. Nkonga
   Behavior of the finite volumes schemes in material and numerical interfaces.
   In Third International Symposium on Finite Volumes for Complex Applications,
   Hermes Science Publications, pages 139-146 (2002)

3. C. Berthon, F. Coquel                                                        (pdf file)
   Nonlinear projection methods for multi-entropies Navier-Stokes systems
   Innovative methods for numerical solutions of partial differential equations (Arcachon, 1998)
   World Sci. Publishing, River Edge, NJ, pp 278--304 (2002)

2. C. Berthon, F. Coquel
   Travelling wave solutions of a convective diffusive system with first and second order terms in nonconservation form.
   Hyperbolic problems: theory, numerics, applications, Vol. I,
   Internat. Ser. Numer. Math., 129, pages 47-54 (1999)

1. C. Berthon, F. Coquel
   Nonlinear projection methods for multi-entropies Navier-Stokes systems.
   Finite volumes for complex applications II : Problems and perspectives,
   Hermes Science Publications, pages 307-314 (1999)

OTHER PUBLICATIONS

1. C. Berthon, S. Clain, F. Foucher, V. Michel-Dansac
   A Bernoulli's relation capturing scheme to simulate the 2011 Japan tsunami
   ECCOMAS Newsletter, July 2020