A. S. Almgren, V. E. Beckner, J. B. Bell, M. S. Day, L. H. Howell et al., CASTRO: a new compressible astrophysicial solver. I. Hydrodynamics and self-gravity, The Astrophysical Journal, vol.715, issue.2, pp.1221-1238, 2010.

. S. Abc-+-98]-a, J. B. Almgren, P. Bell, L. H. Colella, M. L. Howell et al., A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations, Journal of Computational Physics, vol.142, issue.1, pp.1-46, 1998.

A. Abdulle, Fourth order Chebyshev methods with recurrence relation, SIAM Journal on Scientific Computing, vol.23, issue.6, pp.2041-2054, 2002.

A. S. Almgren, J. B. Bell, and W. G. Szymczak, A numerical method for the incompressible Navier-Stokes equations based on an approximate projection, SIAM Journal on Scientific Computing, vol.17, issue.2, pp.358-369, 1996.

A. J. Aspden, M. S. Day, and J. B. Bell, Turbulence-chemistry interaction in lean premixed hydrogen combustion, Proceedings of the Combustion Institute, vol.35, pp.1321-1329, 2015.

P. R. Amestoy, I. S. Duff, J. Koster, and J. Excellent, A fully asynchronous multifrontal solver using distributed dynamic scheduling, SIAM Journal on Matrix Analysis and Applications, vol.23, issue.1, pp.15-41, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00808293

P. R. Amestoy, A. Guermouche, J. Excellent, and S. Pralet, Hybrid scheduling for the parallel solution of linear systems, Parallel Computing, vol.32, issue.2, pp.136-156, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00358623

A. L. Araujo, A. Murua, and J. M. Sanz-serna, Symplectic methods based on decompositions, SIAM Journal on Numerical Analysis, vol.34, issue.5, pp.1926-1947, 1997.

U. Ascher and L. Petzold, Computer methods for Ordinary Differential Equations and Differential-Algebraic Equations, Society for Industrial and Applied Mathematics, 1998.

U. M. Ascher, S. J. Ruuth, and B. T. Wetton, Implicit-Explicit methods for time-dependent Partial Differential Equations, SIAM Journal on Numerical Analysis, vol.32, issue.3, pp.797-823, 1995.

A. Abdulle and G. Vilmart, PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise, Journal of Computational Physics, vol.242, pp.869-888, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00739757

S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune et al.,

R. T. Mcinnes, T. Mills, K. Munson, P. Rupp, B. F. Sanan et al., PETSc users manual, 2019.

]. S. +-19b, S. Balay, M. F. Abhyankar, J. Adams, P. Brown et al., , 2019.

M. J. Berger and P. Colella, Local Adaptive Mesh Refinement for shock hydrodynamics, Journal of Computational Physics, vol.82, issue.1, pp.64-84, 1989.

. B. Bda-+-06]-j, M. S. Bell, A. Day, M. Almgren, C. Lijewski et al., Simulation of lean premixed turbulent combustion, Journal of Physics: Conference Series, vol.46, issue.1, 2006.

J. B. Bell, M. S. Day, and J. F. Grcar, Numerical simulation of premixed turbulent methane combustion, Proc. Combust. Inst, vol.29, issue.2, 1987.

J. B. Bell, M. S. Day, J. F. Grcar, M. J. Lijewski, J. F. Driscoll et al., Numerical simulation of a laboratory-scale turbulent slot flame, Proc. Combust. Inst, vol.31, issue.1, pp.1299-1307, 2007.

J. B. Bell, M. S. Day, I. G. Shepherd, M. R. Johnson, R. K. Cheng et al., Numerical References 219 simulation of a laboratory-scale turbulent V-flame, BDS + 05, vol.102, pp.10006-10011, 2005.

M. J. Berger, Adaptive Mesh Refinement for hyperbolic differential equations, 1982.

M. Benzi, G. H. Golub, and J. Liesen, Numerical solution of saddle point problems, Acta Numerica, vol.14, pp.1-137, 2005.

S. Balay, W. D. Gropp, L. C. Mcinnes, and B. F. Smith, Efficient management of parallelism in Object Oriented numerical software libraries, Modern Software Tools in Scientific Computing, pp.163-202, 1997.

B. L. Bihari and A. Harten, Multiresolution schemes for the numerical solution of 2D conservation laws I, SIAM Journal on Scientific Computing, vol.18, issue.2, pp.315-354, 1996.

I. Bermejo-moreno, J. Bodart, J. Larsson, B. Barney, J. Nichols et al., Solving the compressible navier-stokes equations on up to 1.97 million cores and 4.1 trillion grid points, International Conference for High Performance Computing, Networking, Storage and Analysis, 2013.

M. Berger and J. Oliger, Adaptive mesh refinement for hyperbolic partial differential equations, Journal of Computational Physics, vol.53, issue.3, pp.484-512, 1984.

F. Brezzi and J. Pitkäranta, On the stabilization of finite element approximations of the Stokes equations, Proceedings of a GAMM-Seminar Kiel. Notes on Numerical Fluid Mechanics, vol.10, pp.11-19, 1984.

O. Botella and R. Peyret, Benchmark spectral results on the liddriven cavity flow, Computers and Fluids, vol.27, issue.4, pp.421-433, 1998.

B. A. Bennett and M. D. Smooke, Local rectangular refinement with application to nonreacting and reacting fluid flow problems, Journal of Computational Physics, vol.151, issue.2, pp.684-727, 1999.

W. D. Baines and J. S. Turner, Turbulent buoyant convection from a source in a confined region, Journal of Fluid Mechanics, vol.37, issue.1, pp.51-80, 1969.

J. C. Butcher, Implicit runge-kutta processes, Math. Comp, vol.18, pp.50-64, 1964.

C. Burstedde, L. C. Wilcox, and O. Ghattas, p4est: Scalable algorithms for parallel adaptive mesh refinement on forests of octrees, SIAM Journal on Scientific Computing, vol.33, issue.3, pp.1103-1133, 2011.

. H. Ccds-+-09]-j, A. Chen, B. Choudhary, M. Supinski, E. R. Devries et al., Terascale direct numerical simulations of turbulent combustion using s3d, Computational Science & Discovery, vol.2, issue.1, p.15001, 2009.

A. Cohen, W. Dahmen, and R. Devore, Adaptive Wavelet Techniques in Numerical Simulation, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00018281

A. Cohen, I. Daubechies, and J. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure and Applied Math, vol.45, issue.5, pp.485-560, 1992.

E. Chénier, R. Eymard, T. Gallouët, and R. Herbin, An extension of the MAC scheme to locally refined meshes : convergence analysis for the full tensor time-dependent navier-stokes equations, Calcolo, vol.52, issue.1, pp.69-107, 2014.

E. Chénier, R. Eymard, and R. Herbin, A collocated finite volume scheme to solve free convection for general non-conforming grids, J. Comput. Physics, vol.228, pp.2296-2311, 2009.

E. Chénier, R. Eymard, and O. Touazi, Numerical results using a colocated finite-volume scheme on unstructured grids for incompressible fluid flows, Numerical Heat Transfer, vol.49, issue.3, pp.259-276, 2006.

C. F. Curtiss and J. O. Hirschfelder, Integration of stiff equations, Proceedings of the National Academy of Sciences, vol.38, issue.3, pp.235-243, 1952.

J. H. Chen, Petascale direct numerical simulation of turbulent combustion-fundamental insights towards predictive models, Proceedings of the Combustion Institute, vol.33, pp.99-123, 2011.

A. Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of Computation, vol.22, pp.745-762, 1968.

S. H. Chou and D. Y. Kwak, A covolume method based on rotated bilinears for the generalized Stokes problem, SIAM Journal on Numerical Analysis, vol.35, issue.2, pp.494-507, 1998.

A. Cohen, S. M. Kaber, S. Muller, and M. Postel, Fully adaptive multiresolution finite volume schemes for conservation laws, Mathematics of computation, vol.72, issue.241, 2003.

G. Dahlquist, A special stability problem for linear multistep methods, Nordisk Tidskr. Informations-Behandling, vol.3, pp.27-43, 1963.

I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure and Applied Math, vol.41, issue.7, pp.909-996, 1988.

I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.61, 1992.

M. Day and J. Bell, Numerical simulation of laminar reacting flows with complex chemistry, Combustion Theory and Modelling, vol.4, issue.4, pp.535-556, 2000.

M. S. Day and J. B. Bell, Numerical simulation of laminar reacting flows with complex chemistry, Combust. Theory Modelling, vol.4, pp.535-556, 2000.

M. Duarte, Z. Bonaventura, M. Massot, A. Bourdon, S. Descombes et al., A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations, Computational Plasma Physics, vol.231, pp.1002-1019, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00573043

M. Duarte, Z. Bonaventura, M. Massot, and A. Bourdon, A numerical strategy to discretize and solve the poisson equation on dynamically adapted multiresolution grids for time-dependent streamer discharge simulations, Journal of Computational Physics, vol.289, pp.129-148, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00903307

]. S. Ddd-+-11, M. Descombes, T. Duarte, V. Dumont, M. Louvet et al., Adaptive time splitting method for multi-scale evolutionary partial differential equations, Communications in Nonlinear Science and Numerical Simulation, vol.3, issue.3, pp.1539-1557, 2011.

]. S. Ddd-+-15, M. Descombes, T. Duarte, T. Dumont, V. Guillet et al., Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures, SMAI Journal of Computational Mathematics, vol.3, 2015.

M. Duarte, S. Descombes, C. Tenaud, S. Candel, and M. Massot, Time-space adaptive numerical methods for the simulation of combustion fronts, Combustion and Flame, vol.160, issue.6, pp.1083-1101, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00727442

R. Deiterding, Construction and application of an AMR algorithm for distributed memory computers, Adaptive Mesh Refinement -Theory and Applications, vol.41, pp.361-372, 2005.

R. A. Devore, Nonlinear approximation, Acta Numerica, vol.7, pp.51-150, 1998.

S. Dellacherie, J. Jung, P. Omnes, and P. Raviart, Construction of modified godunov-type schemes accurate at any mach number for the compressible euler system, volume 26 of Mathematical models and methods in ppplied sciences, 2016.

F. Drui, Eulerian modeling and simulations of separated and disperse two-phase flows : development of a unified modeling approach and associated numerical methods for highly parallel computations, 2017.
URL : https://hal.archives-ouvertes.fr/tel-01618320

R. Devore and R. Sharpley, Maximal Functions Measuring Smoothness, Mem. Am. Math. Soc, vol.47, 1984.

V. Daru and C. Tenaud, Numerical simulation of the viscous shock tube problem by using a high resolution monotonicity-preserving scheme, Computers & Fluids, vol.38, issue.3, pp.664-676, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01400427

M. Day, S. Tachibana, J. Bell, M. Lijewski, V. Beckner et al., A combined computational and experimental characterization of lean premixed turbulent low swirl laboratory flames ii. hydrogen flames, DTB + 15, vol.162, pp.2148-2165, 2015.

M. Duarte, Adaptive numerical methods in time and space for the simulation of multi-scale reaction fronts, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00667857

R. Eymard, T. Gallouët, and R. Herbin, Finite volume methods, vol.7, pp.713-1018, 2000.
URL : https://hal.archives-ouvertes.fr/hal-02100732

R. Eymard, T. Gallouët, and R. Herbin, Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces, IMA Journal of Numerical Analysis, vol.30, issue.4, pp.1009-1043, 2010.

B. L. Ehle, On padé approximations to the exponential function and a-stable methods for the numerical solution of initial value problems, 1969.

]. U. Emb-+-06, C. Ebert, T. M. Montijn, W. Briels, B. Hundsdorfer et al., The multiscale nature of streamers, Plasma Sources Sci. Technol, vol.15, pp.118-129, 2006.

F. N. Felten and T. S. Lund, Kinetic energy conservation issues associated with the collocated mesh scheme for incompressible flow, Journal of Computational Physics, vol.215, issue.2, pp.465-484, 2006.

C. J. Forster, Parallel wavelet-adaptive Direct Numerical Simulation of multiphase flows with phase-change, 2016.

J. H. Ferziger and M. Peri?, Computational Methods for Fluid Dynamics, 1999.

L. Freret and C. P. Groth, Anisotropic non-uniform block-based adaptive mesh refinement for three-dimensional inviscid and viscous flows, 22nd AIAA Computational Fluid Dynamics Conference, 2015.

M. P. Gresho and T. S. Chan, On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. part 2: Implementation, International Journal for Numerical Methods in Fluids, vol.11, pp.621-659, 1990.

A. V. Getling, Rayleigh-Bénard convection: structure and dynamcis, volume 11 of Advanced series in nonlinear dynamcis, 1998.

K. Ghia, C. Ghia, and . Shin, High-re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, Journal of Computational Physics, vol.48, issue.3, pp.387-411, 1982.

T. Gallouët, R. Herbin, J. Latché, and K. Mallem, Convergence of the Marker-and-Cell scheme for the incompressible Navier-Stokes equations on non-uniform grids, Foundations of Computational Mathematics, vol.18, issue.1, pp.249-289, 2016.

V. Giovangigli, Multicomponent flow modeling. Modeling and simulation in science, engineering and technology, 1999.

J. Guermond and P. Minev, High-order adaptive time stepping for the incompressible Navier-Stokes equations, SIAM Journal on Scientific Computing, vol.41, p.2019

J. L. Guermond, P. Minev, and J. Shen, An overview of projection methods for incompressible flows, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.6011-6045, 2006.

C. Gear and L. Petzold, ODE methods for the solution of Differential / Algebraic systems, SIAM Journal on Numerical Analysis, vol.21, 1982.

G. Goyal, P. J. Paul, H. S. Mukunda, and S. M. Deshpande, Time dependent operator-split and unsplit schemes for one dimensional premixed flames, Combust. Sci. Technol, vol.60, pp.167-189, 1988.

J. Guermond and L. Quartapelle, On stability and convergence of projection methods based on pressure Poisson equation, International Journal for Numerical Methods in Fluids, vol.26, pp.1039-1053, 1998.

J. Guermond and L. Quartapelle, On the approximation of the unsteady Navier-Stokes equations by finite element projection methods, Numerische Mathematik, vol.80, pp.207-238, 1998.

M. P. Gresho, On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. part 1: Theroy, International Journal for Numerical Methods in Fluids, vol.11, pp.587-620, 1990.

M. P. Gresho and R. L. Sani, On pressure boundary conditions for the incompressible Navier-Stokes equations, International Journal for Numerical Methods in Fluids, vol.7, pp.621-659, 1987.

P. M. Gresho and R. L. Sani, Incompressible flow and the finite element method, advection-diffusion and isothermal laminar flow. Incompressible Flow and the Finite Element Method, 2000.

J. Guermond and J. Shen, Quelques résultats nouveaux sur les méthodes de projection, Comptes Rendus de l'Académie des Sciences -Series I -Mathematics, vol.333, issue.12, pp.1111-1116, 2001.

J. L. Guermond and J. Shen, A new class of truly consistent splitting schemes for incompressible flows, J. Comput. Phys, vol.192, issue.1, pp.262-276, 2003.

A. Guittet, M. Theillard, and F. Gibou, A stable projection method for the incompressible Navier-Stokes equations on arbitrary geometries and adaptive quad/octrees, Journal of Computational Physics, vol.292, pp.215-238, 2015.

J. Guermond, Un résultat de convergence d'ordre deux pour l'approximation des équations de Navier-Stokes par projection incrémentale, Comptes Rendus de l'Académie des Sciences -Series I -Mathematics, vol.325, issue.12, pp.1329-1332, 1997.

H. Guillard and C. Viozat, On the behaviour of upwind schemes in the low Mach number limit, Computers and Fluids, vol.28, issue.1, pp.63-86, 1999.
URL : https://hal.archives-ouvertes.fr/hal-01534938

A. Harten, Adaptive multiresolution schemes for shock computations, Journal of Computational Physics, vol.115, issue.2, pp.319-338, 1994.

A. Harten, Multiresolution representation and numerical algorithms: A brief review. ICASE Rep, pp.94-59, 1994.

A. Harten, Multiresolution algorithms for the numerical solution of hyperbolic conservation laws, Communications on Pure and Applied Mathematics, vol.48, issue.12, pp.1305-1342, 1995.

L. H. Howell, J. B. Bell-;-e, O. Hawkes, H. Chatakonda, A. R. Kolla et al., A petascale Direct Numerical Simulation study of the modelling of flame wrinkling for large-eddy simulations in intense turbulence, SIAM Journal on Scientific Computing, vol.18, issue.4, pp.2690-2703, 1997.

G. R. Hunt and N. B. Kaye, Lazy plumes, Journal of Fluid Mechanics, vol.533, pp.329-338, 2005.

E. Hairer, C. Lubich, and M. Roche, The numerical solution of Differential-Algebraic systems by Runge-Kutta methods. Lectures notes in mathematics, 1989.

E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I, pages xiv+480, 1987.

F. Harlow and J. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Physics of Fluids, vol.8, pp.2182-2189, 1965.

E. Hairer and G. Wanner, Solving ordinary differential equations II. Springer series in computational mathematics, 1996.

E. Hairer and G. Wanner, Stiff differential equations solved by Radau methods, Journal of Computational and Applied Mathematics, vol.111, issue.1, pp.93-111, 1999.

S. Jones and A. Lichtl, GPUs to Mars, full scale simulation of SapceX's Mars rocket engine, Proceedings of the GPU Technology Conference, 2015.

C. A. Kennedy and M. H. Carpenter, Additive Runge-Kutta schemes for convection-diffusion-reaction equations, Applied Numerical Mathematics, vol.44, issue.1, pp.139-181, 2003.

C. Kennedy and M. Carpenter, Diagonally Implicit Runge-Kutta methods for Ordinary Differential Equations. A review, 2016.

J. Kim and P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations, Journal of Computational Physics, vol.59, issue.2, pp.308-323, 1985.

O. M. Knio, H. N. Najm, and P. S. Wyckoff, A semi-implicit numerical scheme for reacting flow. II. Stiff, operator-split formulation, J. Comput. Phys, vol.154, pp.482-467, 1999.

. Ladyzhenskaya, The mathematical theory of viscous incompressible flows, 1969.

H. Leclerc, M. -a.-n'guessan, L. Séries, L. Gouarin, and M. Massot, Parallel dedicated data structures and adaptive multiresolution implementations: application to the resolution of multi-scale PDEs, NASA Technical Memorandum, 2018.

, Summer Program, 2018.

P. Lötstedt and L. Petzold, Numerical solution of nonlinear differential equations with algebraic constraints I: convergence results for backward differentiation formulas, Mathematics of Computation, vol.46, issue.174, pp.491-516, 1986.

P. Lötstedt and L. Petzold, Numerical solution of nonlinear differential equations with algebraic constraints II: practical implications, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.3, pp.720-733, 1986.

S. Mallat, Multiresolution approximation and wavelets orthonormal bases of L 2 (R), Trans. Amer. Math. Soc, vol.315, pp.69-87, 1989.

D. F. Martin and P. Colella, A cell-centered adaptive projection method for the incompressible euler equations, Journal of Computational Physics, vol.163, issue.2, pp.271-312, 2000.

C. Min and F. Gibou, A second order accurate projection method for the incompressible Navier-Stokes equations on non-graded adaptive grids, J. Comput. Phys, vol.219, issue.2, pp.912-929, 2006.

M. Massot, S. Génieys, T. Dumont, and V. A. Volpert, Interaction of thermal explosion and natural convection: critical conditions and new oscillating regimes, SIAM Journal of Applied Mathematics, vol.63, pp.351-372, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00232991

Y. Morinishi, T. S. Lund, O. V. Vasilyev, and P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, Journal of Computational Physics, vol.143, issue.1, pp.90-124, 1998.

A. Madja and J. Sethian, The derivation and numerical solution of the equations for Zero Mach Number combustion, Combustion Science and Technology, vol.42, issue.3-4, pp.185-205, 1985.

R. K. Mohammed, M. A. Tanoff, M. D. Smooke, A. M. Schaffer, and M. B. Long, Computational and experimental study of a forced, time varying, axisymmetric, laminar diffusion flame, References Symposium (International) on Combustion, vol.27, pp.693-702, 1998.

L. Nishant-narechania, C. Freret, and . Groth, Block-based anisotropic AMR with a posteriori adjoint-based error estimation for three-dimensional inviscid and viscous flows, 23rd AIAA Computational Fluid Dynamics Conference, 2017.

S. A. Northrup and C. P. Groth, Solution of laminar combusting flows using a parallel implicit Adaptive Mesh Refinement algorithm, Computational Fluid Dynamics, pp.341-346, 2006.

R. A. Nicolaides, Analysis and convergence of the MAC scheme I. The linear problem, SIAM Journal on Numerical Analysis, vol.29, issue.6, pp.1579-1591, 1992.

F. Nicoud, Conservative high-order Finite-Difference schemes for low-Mach number flows, Journal of Computational Physics, vol.158, issue.1, pp.71-97, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00910303

H. N. Najm and O. M. Knio, Modeling Low Mach number reacting flow with detailed chemistry and transport, J. Scientific Computing, vol.25, issue.1/2, pp.263-287, 2005.

M. N'guessan, M. Massot, L. Séries, and C. Tenaud, High order time integration and mesh adaptation with error control for incompressible Navier-Stokes and scalar transport resolution on dual grids, Journal of Computational and Applied Mathematics, p.112542, 2019.

M. N'guessan, L. Séries, C. Tenaud, and M. Massot, A highorder runge-kutta method coupled to a multiresolution strategy to solve the incompressible Navier-Stokes equations, NASA Technical Memorandum, Proceedings of the 2018 Summer Program, 2018.

P. Syvert, A. Nørsett, and . Wolfbrandt, Attainable order of rational approximations to the exponential function with only real poles, BIT Numerical Mathematics, vol.17, issue.2, pp.200-208, 1977.

R. A. Nicolaides and X. Wu, Analysis and convergence of the MAC scheme II, Navier-Stokes equations. Mathematics of Computation, vol.65, pp.29-44, 1996.

H. N. Najm and P. S. Wyckoff, Premixed flame response to unsteady strain rate and curvature, Combustion and Flame, vol.110, issue.1, pp.92-112, 1997.

H. N. Najm, P. S. Wyckoff, and O. M. Knio, A semi-implicit numerical scheme for reacting flow. I. stiff chemistry, J. Comput. Phys, vol.143, pp.381-402, 1998.

H. N. Najm, P. S. Wyckoff, and O. M. Knio, A semi-implicit numerical scheme for reacting flow: II. stiff, operator-split formulation, Journal of Computational Physics, vol.154, issue.2, pp.428-467, 1999.

S. A. Orszag, M. Israeli, and M. O. Deville, Boundary conditions for incompressible flows, Journal of Scientific Computing, vol.1, issue.1, pp.75-111, 1986.

S. V. Patankar, Numerical heat transfer and fluid flow, Series on Computational Methods in Mechanics and Thermal Science, 1980.

L. Petzold, Differential / Algebraic equations are not ODE's

, SIAM J. Sci. Stat. Comput, vol.3, issue.3, pp.367-384, 1982.

R. B. Pember, L. H. Howell, J. B. Bell, P. Colella, W. Y. Crutchfield et al., An adaptive projection method for unsteady, low-Mach number combustion, Combustion Science and Technology, vol.140, issue.1-6, pp.123-168, 1998.

S. Popinet, Gerris: a tree-based adaptive solver for the incompressible euler equations in complex geometries, Journal of Computational Physics, vol.190, issue.2, pp.572-600, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01445436

M. Postel, Approximations multiéchelles, École de printemps de mécanique des fluides numérique, 2001.

M. Postel, Approximations multiéchelles, Neuvième École Mécanique des Fluides Numérique, pp.1-59, 2005.

A. Prothero and . Robinson, On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential References equations, Mathematics of Computation -Math. Comput, vol.28, pp.145-145, 1974.

L. Pareschi and G. Russo, Implicit-Explicit Runge-Kutta schemes for stiff systems of differential equations, vol.3, pp.269-288, 2001.

R. Rannacher, On Chorin's projection method for incompressible Navier-Stokes cquations, vol.1530, pp.167-183, 2006.

M. Rhie and W. Chow, Numerical study of the turbulent flow past an airfoil with trailing edge separation, AIAA Journal, vol.21, pp.1525-1532, 1983.

Z. Ren and S. B. Pope, Second-order splitting schemes for a class of reactive systems, J. Comput. Phys, vol.227, issue.17, pp.8165-8176, 2008.

R. Ranjan and C. Pantano, A collocated method for the incompressible Navier-Stokes equations inspired by the box scheme, J. Comput. Phys, vol.232, issue.1, pp.346-382, 2013.

J. Reveillon, C. Pera, and Z. Bouali, Examples of the potential of DNS for the understanding of reactive multiphase flows, International Journal of Spray Combustion Dynamics, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00481913

O. Roussel and K. Schneider, An adaptive multiresolution method for combustion problems: Application to flame ball-vortex interaction, Computers & Fluids, vol.34, issue.7, pp.817-831, 2005.

Y. Saad, Iterative methods for sparse linear systems, Society for Industrial and Applied Mathematics, 2003.

B. Sanderse, Energy-conserving runge-kutta methods for the incompressible Navier-Stokes equations, J. Comput. Phys, vol.233, pp.100-131, 2013.

A. Schmidt, A multi-mesh finite element method for phasefield simulations, Interface and Transport Dynamics, pp.208-217, 2003.

A. Schmidt, A multi-mesh finite element method for 3D phase field simulations, Free Boundary Problems, pp.293-301, 2004.

S. Shashank, High fidelity simulations of reactive liquid-fuel jets, 2012.

J. Shen, On error estimates of projection methods for Navier-Stokes equations: first-order schemes, SIAM Journal on Numerical Analysis, vol.29, issue.1, pp.57-77, 1992.

J. Shen, On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes, Mathematics of Computation, vol.65, issue.215, pp.1039-1065, 1996.

D. A. Schwer, P. Lu, W. H. Green, and V. Semião, A consistentsplitting approach to computing stiff steady-state reacting flows with adaptive chemistry, Combust. Theory Modelling, vol.7, issue.2, pp.383-399, 2003.

J. Shashank, G. Larsson, and . Iaccarino, A co-located incompressible Navier-Stokes solver with exact mass, momentum and kinetic energy conservation in the inviscid limit, J. Comput. Physics, vol.229, pp.4425-4430, 2010.

M. A. Singer, S. B. Pope, and H. N. Najm, Operator-splitting with ISAT to model reacting flow with detailed chemistry, Combust. Theory Modelling, vol.10, issue.2, pp.199-217, 2006.

C. Safta, J. Ray, and H. N. Najm, A high-order low-Mach number AMR construction for chemically reacting flows, Journal of Computational Physics, vol.229, issue.24, pp.9299-9322, 2010.

G. Strang, Accurate partial difference methods. I. Linear Cauchy problems, Arch. Ration. Mech. Anal, vol.12, pp.392-402, 1963.

G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal, vol.5, pp.506-517, 1968.

F. Tholin and A. Bourdon, Influence of the external electrical circuit on the regimes of a nanosecond repetitively pulsed discharge in air at atmospheric pressure, Plasma Physics and Controlled Fusion, vol.57, issue.1, p.14016, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01348455

C. Tenaud and M. Duarte, Tutorials on adaptive multiresolution for mesh refinement applied to fluid dynamics and reactive media problems, ESAIM: Proc, vol.34, pp.184-239, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01618392

R. Temam, Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires. Archive for Rational Mechanics and Analysis, vol.32, pp.135-153, 1969.

R. ;. Temam, G. Papanicolaou, and R. T. Rockafellar, Navier-Stokes Equations: Theory and Numerical Analysis. Studies in Mathematics and its Applications. Lions, 1977.

C. Tenaud, An adaptive multiresolution technique for unsteady compressible flow simulations, In Symposium on Applied Aerodynamics, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01629410

L. Timmermans, P. D. Minev, and F. Van-de-vosse, An approximate projection scheme for incompressible flow using spectral elements, International Journal for Numerical Methods in Fluids, vol.22, pp.673-688, 1996.

S. Turek, Efficient Solvers for Incompressible Flow Problems: An Algorithmic and Computational Approach, 1998.

H. Uzawa, K. J. Arrow, and L. Hurwicz, Studies in non-linear programming, 1958.

J. Van-kan, A second-order accurate pressure-correction scheme for viscous incompressible flow, Siam Journal on Scientific and Statistical Computing, vol.7, 1986.

P. A. Vitello, B. M. Penetrante, and J. N. Bardsley, Simulation of negative-streamer dynamics in nitrogen, Physical Review E, vol.49, pp.5574-5598, 1994.

Q. Wargnier, Mathematical modeling and simulation of nonequilibrium plasmas: application to magnetic reconnection in the Sun atmosphere, 2019.
URL : https://hal.archives-ouvertes.fr/tel-02500745

R. Williams, K. Burrage, I. Cameron, and M. Kerr, A four-stage index 2 Diagonally Implicit Runge-Kutta method, Applied Numerical Mathematics, vol.40, issue.3, pp.415-432, 2002.

B. Yang and S. B. Pope, An investigation of the accuracy of manifold methods and splitting schemes in the computational implementation of combustion chemistry, Combust. and Flame, vol.112, issue.1-2, pp.16-32, 1998.

]. W. Zab-+-19, A. Zhang, V. Almgren, J. Beckner, J. Bell et al., Amrex: a framework for block-structured adaptive mesh refinement, Journal of Open Source Software, vol.4, p.1370, 2019.

]. W. Zha-+-11, L. Zhang, A. Howell, A. Almgren, J. Burrows et al., CASTRO: a new compressible astrophysical solver. II. Gray radiation hydrodynamics, The Astrophysical Journal Supplement Series, 2011.

]. W. Zha-+-12, L. Zhang, A. Howell, A. Almgren, J. Burrows et al., CASTRO: a new compressible astrophysical solver. III. Multigroup radiation hydrodynamics, The Astrophysical Journal Supplement Series, p.204, 2012.

Y. Zang, R. Street, and J. Koseff, A non-staggered grid, fractional step method for time-dependent incompressible Navier-Stokes equations in curvilinear coordinates, Journal of Computational Physics, vol.114, issue.1, pp.18-33, 1994.