1 2 3 4 5 6 7 8
  1. Articles in journals
  2. Editorial activities
  3. Comptes Rendus de l'Académie des Sciences
  4. Papers in revision
  5. Submitted papers
  6. Refereed conferences
  7. Chapters of books
  8. Invited lectures




Articles in journals
Multicomponent and multiphase problems
  1. Rémi Abgrall, Generalisation of the Roe scheme for the computation of mixture of perfect gases. Rech. Aérospatiale (English edition), 1988--6:31--43, Décembre 1988.
  2. Rémi Abgrall and Jean-Louis Montagné. Generalization of the Osher scheme for calculating flows of mixed gases of variable concentrations, and of real gases.  Rech. Aérospatiale, (4):1--13, 1989.
  3. Rémi Abgrall. An extension of Roe's upwind scheme to algebraic equilibrium real gas models.  Comput.  & Fluids, 19(2):171--182, 1991.
  4. Rémi Abgrall, Hypersonic calculations by Riemann solvers techniques. Comput. Phys. Commun., 65(1-3):1--7, 1991.
  5. Rémi Abgrall, Loula Fezoui, and Jean Talandier.An extension of Osher's Riemann solver for chemical and vibrational non- equilibrium gas flows. Int. J. Numer. Methods Fluids, 14(8):935--960, 1992.
  6. Didier Chargy, Rémi Abgrall, Loula Fézoui, and Bernard Larrouturou.Conservative numerical schemes for multicomponent inviscid flows. Rech. Aérospat., (2):61--80, 1992
  7. Rémi Abgrall. How to prevent pressure oscillations in multicomponent flow calculations: a quasi-conservative approach.  J. Comput. Phys., 125(1):150--160, 1996
  8. Richard Saurel and Rémi Abgrall. A simple method for compressible multifluid flows. SIAM J. Sci. Comput., 21(3):1115--1145, 1999.
  9. Richard Saurel and Rémi Abgrall. A multiphase Godunov method for compressible multifluid and  multiphase flows. J. Comput. Phys., 150(2):425--467, 1999.
  10. Rémi Abgrall and Smadar Karni. Computations of compressible multifluids. J. Comput. Phys., 169(2):594--623, 2001.
  11. Jacques Massoni, Richard Saurel, Boniface Nkonga, and Rémi Abgrall. Some models and Eulerian methods for interface problems between  compressible fluids with heat transfer. (Proposition de méthodes et modèles eulériens pour les problèmes à  interfaces entre fluides compressible en présence de transfert de chaleur.).  Int. J. Heat Mass Transfert, 45(6):1287--1307, 2002.
  12. Germain Billet and Rémi Abgrall. An adaptive shock-capturing algorithm for solving unsteady reactive flows.  Comput. Fluids, 32(10):1473--1495, 2003.
  13. Rémi Abgrall, Boniface Nkonga, and Richard Saurel. Efficient numerical approximation of compressible multi-material flow for unstructured meshes. Comput. & Fluids, 32(4):571--605, 2003
  14. Rémi Abgrall and Richard Saurel. Discrete equations for physical and numerical compressible multiphase mixtures. J. Comput. Phys., 186(2):361--396, 2003.
  15. R. Abgrall, M. Papin, and L. Hallo, A scheme for compressible two-phase flows and interface problems. Chen, Zhangxin (ed.) et al., Current trends in scientific computing. ICM 2002 Beijing satellite conference on scientific computing, August 15--18, 2002, Xi'an, China. Providence, RI: American Mathematical Society (AMS).  Contemp. Math. 329, 1-12 (2003).
  16. Rémi Abgrall and Vincent Perrier. Asymptotic expansion of a multiscale numerical scheme for compressible multiphase flows. SIAM Multiscale and Modelisation in Science, 5(1):84--115, 2006.
  17. Richard Saurel,  Fabien Petitpas and  Remi Abgrall, Modelling phase transition in metastable liquids: application to cavitating and flashing flows,  J. Fluid Mech., Vol 607, pages 313-350, 2008.
  18. Rémi Abgrall and Smadar Karni, A comment on the computation of non-conservative products.  J. Comput. Phys, vol 229, No 8, pages 2759-2763, 2010
ENO schemes, High order schemes
  1. Rémi Abgrall. An essentially non-oscillatory reconstruction procedure on finite-element type meshes: Application to compressible flows. Comput. Methods Appl. Mech. Eng., 116:95--101, 1994
  2. Rémi Abgrall. On essentially non-oscillatory schemes on unstructured meshes:  Analysis and implementation, J. Comput. Phys. , 114(1):45--58, 1994.
  3. Rémi Abgrall and Thomas Sonar. On the use of Mà¼hlbach expansions in the recovery step of ENO methods. Numer. Math. , 76(1):1--25, 1997.
  4. Rémi Abgrall, Stéphane Lantéri, and Thomas Sonar. ENO approximations for compressible fluid dynamics. ZAMM, Z. Angew. Math. Mech., 79(1):3--28, 1999.
Hamilton Jacobi equations
  1. Rémi Abgrall. Numerical discretization of the first-order Hamilton-Jacobi equation on triangular meshes. Commun. Pure Appl. Math., 49(12):1339--1373, 1996.
  2. Steeve Augoula and Rémi Abgrall. High order numerical discretization for Hamilton-Jacobi equations on triangular meshes.  J. Sci. Comput., 15(2):197--229, 2000.
  3. Rémi Abgrall. Numerical discretization of boundary conditions for first order Hamilton--Jacobi equations. SIAM J. Numer. Anal., 41(6):2233--2261, 2003.
  4. R. Abgrall and V. Perrier, On the numerical approximation of first  order Hamilton Jacobi equations, International Journal of Applied Mathematics and Computer,17(3):403--412, 2007. DOI:10.2478/v100006-007-0033-0
  5. R. Abgrall, Construction of simple, stable and convergent scheme for first order hamilton-Jacobi equations, SIAM J. Sci. Comput., vol 31, No 4, pages 2419-2446, 2009
Multiresolution analysis
  1. Rémi Abgrall and Ami Harten. Multiresolution representation in unstructured meshes. SIAM J. Numer. Anal., 35(6):2128--2146, 1998.
Shallow water equations
  1. Rémi Abgrall and Smadar Karni, Two-layers shallow water equations: a relaxation approach, SIAM J. Sci. Comput., vol 31, No 3, pages 1603-1627, 2009.
Uncertainty quantification
  1. Rémi Abgrall,  A simple, flexible and generic deterministic approach to uncertainty quantifications in non linear problems : application to fluid flow problems, submitted to J. Comput. Phys., also INRIA Report

Residual distribution schemes
  1. Rémi Abgrall. Toward the ultimate conservative scheme: Following the quest.  J. Comput. Phys., 167(2):277--315, 2001.
  2. Rémi Abgrall and Timothy Barth. Residual distribution schemes for conservation laws via adaptive quadrature. SIAM J. Sci. Comput., 24(3):732--769, 2002.
  3. Rémi Abgrall and Philipp L.  Roe, High-order fluctuation schemes on triangular meshes.  J. Sci. Comput., 19(1-3):3--36, 2003.
  4. Rémi Abgrall and Mohamed Mezine. Construction of second order accurate monotone and stable residual distribution schemes for unsteady flow problems.  J. Comput. Phys. , 188(1):16--55, 2003.
  5. Rémi Abgrall and Mohamed Mezine. Construction of second-order accurate monotone and stable residual  distribution schemes for steady problems. J. Comput. Phys., 195(2):474--507, 2004.
  6. Rémi Abgrall, Nikolay¯  Andrianov  and Mohamed  Mezine. Towards very high-order accurate schemes for unsteady convection problems on unstructured meshes. Int. J. Numer. Methods Fluids, 47(8-9):679--691, 2005.
  7. Rémi Abgrall and Fabien Marpeau. Residual distribution schemes on quadrilateral meshes.  J. Scientific Computing, 30(1), 2007
  8. Rémi Abgrall. Essentially non oscillatory residual distribution schemes for hyperbolic problems. J. Comput. Phys., 214(2):773--808, 2006.
  9. Rémi Abgrall. Residual distribution schemes: current status and future trends.  Computer and Fluids, 35(7):641--669, 2006. invited paper
  10. Mario Ricchiuto, Nadège Villedieu, Rémi Abgrall, and Herman Deconinck. On uniformly accurate residual distribution schemes for advection--diffusion problems.  J. Computational and Applied Mathematics, 2008. Volume 215, number 2(1), p 547-556, (doi :http://dx.doi.org/10.1016/j.cam.2006.03.059)
  11. Mario Ricchiutto, Rémi Abgrall, and Hermann Deconinck. Analysis of a class of conservative residual schemes with application to the solution of the shallow water equations on unstructured meshes. J. Comput. Phys., 222(1): 287--331, 2007
  12. Villedieu, N. and Quintino, T. and Abgrall, R. and Deconinck, H.,  High-order residual distribution schemes on quadrilateral meshes.  Int. J. Numer. Methods Fluids, Vol 56, No 8, pages 1559-1566, 2008
  13. R. Abgrall and C.-W. Shu, Development of residual distribution schemes for the discontinuous galerkin schemes : the scalar case with continuous elements,  Communications in Computational Physics,  Vol 5, pages 376-390, 2009.
  14. R. Abgrall, M. Ricchiuto, A. Larat and C. Tavé, A simple construction of  very high order non-oscillatory compact schemes on unstructured meshes, Computers and Fluids, Vol 38, pages 1314-1323, 2009.
  15. Rémi Abgrall, Residual distribution method using discontinuous elements for the computation of possibly non smooth flows, Adv. Appl. Math. Mech., Vol. 2, No 1, 2010.
  16. Mario Ricchiuto, Rémi Abgrall, Explicit Runge–Kutta residual distribution schemes for time dependent problems: Second order case , Journal of Computational Physics, volume 229, issue 16, august 2010, Pages 5653-5691.
  17. R. Abgrall, A. Larat and M. Ricchiuto, Construction of very high order residual distribution schemes for steady inviscid flow problems on hybrid unstructured meshes. Journal of Computational Physics, Available online 12 August 2010
Lagrangian schemes
  1.  Raphaël Loubère, Jean  Ovadia, and Rémi Abgrall. A Lagrangian discontinuous Galerkin-type method on unstructured meshes to solve hydrodynamics problems.  Int. J. Numer. Methods Fluids , 44(6):645--663, 2004.
  2. P.H. Maire, R. Abgrall, J. Breil and J. Ovadia, A cell--centered Lagrangian scheme for two--dimensional compressible flow problems,  SIAM J. on Scientific Computing, vol. 29, number 4, page 1281--1824, 2007. 
  3. F. Vilar, P.H. Maire and R. Abgrall, Cell-centered discontinuous Galerkin discretizations for two-dimensional scalar , conservation laws on unstructured grids and for one-dimensional Lagrangian hydrodynamics, Computers & Fluids, in press, 2011.
Applications
  1. Rémi Abgrall and Jean-David Benamou. Big Ray Tracing and Eikonal Solver on Unstructured Grids:Application to the Computation of a Multi-valued Travel-time Field.  Geophysics, 64(1):230--239, January--February 1999.
  2. Rémi Abgrall, Michel Ravachol, and Séverin Marret. The simulation of the linearized Euler equations by a second order scheme is possible.  Int. J. on Aeroacoustics, 4(1--2):49--68, 2005.
back to top
Editorial activities


  1. Rémi Abgrall and Hermann Deconinck. Special issue on  Residual distribution schemes, discontinuous Galerkin schemes, multidimensional schemes and mesh adaptation. Computer and Fluids, 34(4-5):399--640, 2005.
  2. Rémi Abgrall and Hervé Guillard, Special issue: Low Mach number flows. Selected papers based on the presentation at the international conference, Porquerolles Island, France, June 21--25, 2004.  ESAIM, Math. Model. Numer. Anal. , 39(3):437--621, 2005.
  3. Rémi Abgrall, Jean-Antoine Désideri, Roland Glowinski, Michel Mallet, and Jacques Périaux, editors,  Hypersonic Flows for Reentry Problems, volume II, pages 1131--1144. Springer Verlag, 1993.
back to top
Comptes Rendus de l'Académie des Sciences

  1. Rémi Abgrall and Claude Basdevant. Un schéma numérique semi-lagrangien pour la turbulence bidimensionnelle.  C. R. Acad. Sci. Paris Sér. I Math., 305(7):315--318, 1987.
  2. Rémi Abgrall. Sur le comportement asymptotique des coefficients de certaines approximations polynomiales.  C. R. Acad. Sci. Paris S\'er. I Math., 315(1):97--100, 1992.
  3. Rémi Abgrall. Approximation du problème de Riemann vraiment multidimensionnel des équations d'Euler par une méthode de type Roe. I. La linéarisation. C. R. Acad. Sci. Paris Sér. I Math., 319(5):499--504, 1994.
  4. Rémi Abgrall. Approximation du problème de Riemann vraiment multidimensionnel des équations d'Euler par une méthode de type Roe. II. Solution du problème de Riemann approché.  C. R. Acad. Sci. Paris Sér. I Math., 319(6):625--629, 1994.
  5. Rémi Abgrall, Thierry Colin, and Boniface Nkonga. à‰tude du système de Schrà¶dinger-Bloch modélisant la propagation d'un laser dans un gaz. C. R. Acad. Sci. Paris Sér. I Math., 333(7):689--692, 2001.
  6. Mikaël Papin and Rémi Abgrall. Entropic closure laws for two-fluid seven equation models.  C. R. Acad. Sci. Mécanique, 333(11):838--842, 2005.
back to top

Refereed conferences
 
  1. Rémi Abgrall. Extension of Roe's approximate Riemann solver to equilibrium and non-equilbrium flows. In P.Wesserling, editor, Note on Numerical Fluid Mechanics, number~29 in Lecture Notes in Physics, 1990.
  2. Rémi Abgrall. Calculation of non equilibrium flows in a high enthalpy wind tunnel. In Désideri, Glowinski, and Périaux, editors, Hypersonic Flows for Reentry Problems, volume II, pages 1131--1144. Springer Verlag, 1991.
  3. Rémi Abgrall and Agnès Merlo. Calculation of a viscous hypersonic nozzle flow by an implicit second  order upwind scheme using unstructured meshes. In  Proceedings of the 13th International Conference on Numerical Fluid Dynamics, volume 414, pages 340--344. Springer Verlag, 1992.
  4. Rémi Abgrall and Agnès Merlo. Calculation of an hypersonic nozzle flow by a second order upwind scheme on unstructured meshes. In Abgrall, Désideri, Glowinski, Mallet, and Périaux, editors,  Hypersonic Flows for Reentry Problems, volume~II, pages 1131--1144. Springer Verlag, 1993.
  5. Rémi Abgrall. Multiresolution analysis on unstructured meshes: Application to CFD. In Morton, K. W. (ed.) et al., Numerical methods for fluid dynamics V. Proceedings of the conference, Oxford, UK, April 1995. Oxford: Clarendon Press. 271-277 . 1995.
  6. Rémi Abgrall. A third-order ENO scheme on unstructured meshes. Application to shock wave calculations. In Brun, Raymond (ed.) et al., Shock waves at Marseille I. Hypersonics, shock tube and shock tunnel flow. Proceedings of the 19th international symposium on shock waves, held in Marseille, France, 26-30 July 1993. Berlin: Springer-Verlag. 427-432 . 1995.
  7. Rémi Abgrall. Construction of genuinely multidimensional upwind distributive schemes. In Vilsmeier, Roland (ed.) et al., Finite volumes for complex applications II. Problems and perspectives. Papers from the 2nd international conference, Duisburg, July 19-22, 1999. Paris: Hermes Science Publications. 3-10 . 1999.
  8. Steeve Augoula and Rémi Abgrall. A discontinuous projection algorithm for Hamilton Jacobi equations. In Cockburn, Bernardo (ed.) et al., Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24-26, 1999. Berlin: Springer. Lect. Notes Comput.Sci. Eng. 11, 255-261. 2000.
  9. Rémi Abgrall and Smadar Karni.  Ghost-fluids for the poor: a single fluid algorithm for multifluids. In Hyperbolic problems: theory, numerics, applications, Vol. I, II (Magdeburg, 2000), volume 141 of  Internat. Ser. Numer. Math., 140, pages 1--10. Birkhà¤user, Basel, 2001.
  10. Laurence Gozalo and Rémi Abgrall. A new limiter that improves TVD-MUSCL schemes. In Toro, E. F. (ed.), Godunov methods. Theory and applications. International conference, Oxford, GB, October 1999. New York, NY: Kluwer Academic/ Plenum Publishers. 411-417. 2001.
  11. Rémi Abgrall and Timothy Barth. New results for residual distribution schemes. In Toro, E. F. (ed.), Godunov methods. Theory and applications.  International conference, Oxford, GB, October 1999. New York, NY: Kluwer Academic/ Plenum Publishers. 27-43. 2001.
  12. Rémi Abgrall, Katherine Mer, and Boniface Nkonga. A Lax-Wendroff type theorem for residual schemes. In Hafez, M. M. (ed.) et al., Innovative methods for numerical solutions of partial differential equations. Proceedings of the symposium on  progress in numerical solutions of partial differential equations, Arcachon, France, July 11-13, 1998. In honor of Phil Roe on the occasion of his 60th birthday. Singapore: World Scientific. 243-266 . 2002.
  13. Rémi Abgrall and Mohamed Mezine. A compact residual scheme for unsteady compressible flow problems. In Armfield, S. (ed.) et al., Computational fluid dynamics2002. Proceedings of the second international conference on computational fluid dynamics, ICCFD, Sydney, Australia, July, 15-19, 2002. Berlin: Springer. 165-170 . 2003.
  14. Rémi Abgrall. Multiresolution analysis on unstructured meshes: Application to CFD. Chetverushkin, B. N. (ed.) et al., Experimentation, modelling and computation in flow, turbulence and combustion. Vol. 2. Proceedings of the 3rd French-Russian-Uzbek workshop on Fluid dynamics, Tashkent, Uzbekistan, April 23--28, 1995. Chichester: Wiley. CMAS: Computational Methods in Applied Sciences. 147-156 (1997).}, 1997.
  15. R. Abgrall and V. Perrier,  A Numerical Scheme for Compressible Multiphase Flows,  In Computational Fluid Dynamics 2004, Proceedings of the Third International Conference on Computational Fluid Dynamics, ICCFD3, Toronto, 16 July 2004 Proceedings of the Third International Conference on Computational Fluid Dynamics, ICCFD3, Toronto,  July 2004,  C. Groth and D.W. Zingg editors, Springer Verlag, 2006. doi 0.1007/3-540-31801-1
  16. Rémi Abgrall, Stéphane Galéra, Pietro Congedo and Christophe Corre, A simple semi-intrusive method for Uncertainty Quantification of shocked flows  comparison with a non-intrusive Polynomial Chaos method, ECCOMAS CFD 2010

back to top
Chapters of books
  1. Rémi Abgrall. Some preliminary results in multiresolution analysis on unstructured meshes: Application to CFD. In Chetverushkin, B. N. (ed.) et al., Experimentation, modelling and computation in flow, turbulence and combustion. Vol. 2. Proceedings of the 3rd French-Russian-Uzbek workshop on Fluid dynamics, Tashkent, Uzbekistan, April 23--28, 1995. Chichester: Wiley. CMAS: Computational Methods in Applied Sciences. 147-156 . 1997.
  2. Rémi Abgrall. Upwind and High Resolution Schemes, chapter: Design of an Essentially Non Oscilatory reconstruction procedure for finite element type meshes, pages 519--549. Springer Verlag, 1998.
  3. Rémi Abgrall, Thomas Sonar, Oliver Friedrich, and Germain Billet. High order approximations for compressible fluid dynamics on unstructured and Cartesian meshes. In Barth, Timothy J. (ed.) et al., High-order methods for computational physics. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 9, 1-67. 1999.
  4. Rémi Abgrall.  New advances in Computational Fluid Dynamics: Theory, Methods and Applications, volume~2 of  Series in Contemporary Applied Mathematics, chapter Residual distributive schemes for compressible flows. Higher education press, Pekin, Chine, 2001. Proceeding d'une conf\'erence tenue à  Xian, RP Chine, du 6 au 17 septembre 2000.
back to top
Invited Lectures
  1. Rémi Abgrall and Frédéric Lafon. ENO schemes on unstructured meshes. In Lecture series 1993-04. von Karman Institute, 1993.
  2. Rémi Abgrall and Mohamed Mezine. Residual distribution schemes for steady problems. In  von Kà rman Institute Lecture Series, March 2003.
  3. Mohamed Mezine, Mario Ricchiuto, Rémi Abgrall, and Hermann Deconinck. Monotone and stable residual distribution schemes on prismatic  space--time elements for unsteady conservation laws. In  von Kà rman Institute Lecture Series, March 2003.
  4. Mario Ricchiuto, Rémi Abgrall, and Hermann Deconinck.Very high order fluctuation splitting schemes for unsteady scalar advection. In  von Kà rman Institute Lecture Series, March 2003.
  5. Hermann Deconinck and Rémi  Abgrall. Introduction to residual distribution methods. In  CFD--higher order discretization methods. von Kà rman Institute, 2005.
  6. Mario Ricchiuto, Nadège Villedieu, Rémi Abgrall, and Hermann Deconinck. High--order residual distribution schemes: discontinuity capturing crosswind dissipation and extension to advection--diffusion. In  CFD--higher order discretization methods. von Karman Institute, 2005.
  7. Rémi Abgrall. Construction of high--order residual distribution schemes for scalar problems, preliminary results for systems. In  CFD--higher order discretization methods. von Kàrman Institute, 2005.

Misc
  1. Rémi et Sophie Abgrall, Simulation Numérique, que reste-t-il à découvrir ? Tribune libre, Innovation technologique, 2010