M. L. Adams, Discontinuous Finite Element Transport Solutions in Thick Diffusive Problems, Nuclear Science and Engineering, vol.137, issue.3, pp.298-333, 2001.
DOI : 10.13182/NSE00-41

W. Alt, Biased random walk models for chemotaxis and related diffusion approximations, Journal of Mathematical Biology, vol.137, issue.2, pp.147-177, 1980.
DOI : 10.1007/BF00275919

G. Bispen, K. R. Arun, M. Luk-?-ov-medvid-?-ov, and S. Noelle, Abstract, Communications in Computational Physics, vol.26, issue.02, pp.307-347, 2014.
DOI : 10.1016/j.advwatres.2009.12.006

R. Botchorishvili, B. Perthame, and A. Vasseur, Equilibrium schemes for scalar conservation laws with stiff sources, Mathematics of Computation, vol.72, issue.241, pp.131-157, 2003.
DOI : 10.1090/S0025-5718-01-01371-0

J. Antonio, C. , and B. Yan, An asymptotic preserving scheme for the diffusive limit of kinetic systems for chemotaxis, Multiscale Model. Simul, vol.11, issue.1, pp.336-361, 2013.

F. Chalub, P. Markowich, B. Perthame, and C. Schmeiser, Kinetic Models for Chemotaxis and their Drift-Diffusion Limits, Monatshefte f???r Mathematik, vol.142, issue.1-2, pp.123-141, 2004.
DOI : 10.1007/s00605-004-0234-7

S. Chandrasekhar, Radiative transfer, 1960.

C. Di-russo, R. Natalini, and M. Ribot, Global existence of smooth solutions to a two-dimensional hyperbolic model of chemotaxis, Commun. Appl. Ind. Math, vol.1, issue.1, pp.92-109, 2010.

C. Emako, L. Neves-de-almeida, and N. Vauchelet, Existence and diffusive limit of a two-species kinetic model of chemotaxis. Kinetic and Related Models, pp.359-380, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00980594

F. Filbet and S. Jin, A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources, Journal of Computational Physics, vol.229, issue.20, pp.7625-7648, 2010.
DOI : 10.1016/j.jcp.2010.06.017
URL : https://hal.archives-ouvertes.fr/hal-00659668

F. Filbet and C. Yang, Numerical Simulations of Kinetic Models for Chemotaxis, SIAM Journal on Scientific Computing, vol.36, issue.3, pp.348-366, 2014.
DOI : 10.1137/130910208
URL : https://hal.archives-ouvertes.fr/hal-00798822

L. Gosse, Transient radiative transfer in the grey case: Well-balanced and asymptotic-preserving schemes built on Case's elementary solutions, Journal of Quantitative Spectroscopy and Radiative Transfer, vol.112, issue.12, 1995.
DOI : 10.1016/j.jqsrt.2011.04.003

L. Gosse, Asymptotic-Preserving and Well-Balanced schemes for the 1D Cattaneo model of chemotaxis movement in both hyperbolic and diffusive regimes, Journal of Mathematical Analysis and Applications, vol.388, issue.2, pp.964-983, 2012.
DOI : 10.1016/j.jmaa.2011.10.039

L. Gosse, A well-balanced scheme for kinetic models of chemotaxis derived from one-dimensional local forward???backward problems, Mathematical Biosciences, vol.242, issue.2, pp.117-128, 2013.
DOI : 10.1016/j.mbs.2012.12.009
URL : https://hal.archives-ouvertes.fr/hal-00651430

H. Hwang, K. Kang, and A. Stevens, Drift-diffusion limits of kinetic models for chemotaxis: a generalization, Discrete Contin. Dyn. Syst. Ser. B, vol.5, issue.2, pp.319-334, 2005.

S. Jin, Asymptotic preserving (ap) schemes for multiscale kinetic and hyperbolic equations: a review. lecture notes for summer school on methods and models of kinetic theory, 2010.

M. Shi-jin, H. Tang, and . Han, A uniformly second order numerical method for the one-dimensional discrete-ordinate transport equation and its diffusion limit with interface, Networks and Heterogeneous Media, vol.4, issue.1, pp.35-65, 2009.
DOI : 10.3934/nhm.2009.4.35

S. Jin and X. Shi, An efficient method for computing hyperbolic systems with geometrical source terms having concentrations, J. Comput. Math, vol.22, issue.2, pp.230-249, 2004.

F. Evelyn, L. A. Keller, and . Segel, Model for chemotaxis, Journal of Theoretical Biology, vol.30, issue.2, pp.225-234, 1971.

P. Kubelka, New Contributions to the Optics of Intensely Light-Scattering Materials Part I, Journal of the Optical Society of America, vol.38, issue.5, pp.448-457, 1948.
DOI : 10.1364/JOSA.38.000448

A. Kurganov and D. Levy, Central-Upwind Schemes for the Saint-Venant System, ESAIM: Mathematical Modelling and Numerical Analysis, vol.36, issue.3, pp.397-425, 2002.
DOI : 10.1051/m2an:2002019

E. W. Larsen and J. E. , Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II, Journal of Computational Physics, vol.83, issue.1, pp.212-236, 1989.
DOI : 10.1016/0021-9991(89)90229-5

W. Edward, J. Larsen, W. Morel, and . Jr, Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes, Journal of Computational Physics, vol.69, issue.2, pp.283-324, 1987.

R. J. Leveque, Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm, Journal of Computational Physics, vol.146, issue.1, pp.346-365, 1998.
DOI : 10.1006/jcph.1998.6058

L. Mieussens, On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models, Journal of Computational Physics, vol.253, pp.138-156, 2013.
DOI : 10.1016/j.jcp.2013.07.002
URL : https://hal.archives-ouvertes.fr/hal-00772684

R. Natalini, M. Ribot, and M. Twarogowska, A well-balanced numerical scheme for a one-dimensional quasilinear hyperbolic model of chemotaxis, Communications in Mathematical Sciences, vol.12, issue.1, pp.13-39, 2014.
DOI : 10.4310/CMS.2014.v12.n1.a2
URL : https://hal.archives-ouvertes.fr/hal-00764086

H. Othmer, S. Dunbar, and W. Alt, Models of dispersal in biological systems, Journal of Mathematical Biology, vol.25, issue.3, pp.263-298, 1988.
DOI : 10.1007/BF00277392

H. Othmer and T. Hillen, The Diffusion Limit of Transport Equations II: Chemotaxis Equations, SIAM Journal on Applied Mathematics, vol.62, issue.4, pp.1222-1250, 2002.
DOI : 10.1137/S0036139900382772

B. Perthame and C. Simeoni, A kinetic scheme for the Saint-Venant system??with a source term, Calcolo, vol.38, issue.4, pp.201-231, 2001.
DOI : 10.1007/s10092-001-8181-3
URL : https://hal.archives-ouvertes.fr/hal-00922664

J. Saragosti, V. Calvez, N. Bournaveas, A. Buguin, P. Silberzan et al., Mathematical Description of Bacterial Traveling Pulses, PLoS Computational Biology, vol.33, issue.8, pp.1000890-1000902, 2010.
DOI : 10.1371/journal.pcbi.1000890.s001
URL : https://hal.archives-ouvertes.fr/hal-00440108

J. Saragosti, V. Calvez, N. Bournaveas, B. Perthame, A. Buguin et al., Directional persistence of chemotactic bacteria in a traveling concentration wave, Proceedings of the National Academy of Sciences, vol.108, issue.39, pp.16235-16240, 2011.
DOI : 10.1073/pnas.1101996108
URL : https://hal.archives-ouvertes.fr/hal-00789064

W. Sun, S. Jiang, and K. Xu, An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations, Journal of Computational Physics, vol.285, pp.265-279, 2015.
DOI : 10.1016/j.jcp.2015.01.008

K. Xu, A Gas-Kinetic BGK Scheme for the Navier???Stokes Equations and Its Connection with Artificial Dissipation and Godunov Method, Journal of Computational Physics, vol.171, issue.1, pp.289-335, 2001.
DOI : 10.1006/jcph.2001.6790

K. Xu, A Well-Balanced Gas-Kinetic Scheme for the Shallow-Water Equations with Source Terms, Journal of Computational Physics, vol.178, issue.2, pp.533-562, 2002.
DOI : 10.1006/jcph.2002.7040

K. Xu and J. Huang, A unified gas-kinetic scheme for continuum and rarefied flows, Journal of Computational Physics, vol.229, issue.20, pp.7747-7764, 2010.
DOI : 10.1016/j.jcp.2010.06.032