- 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.
- 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.
- Rémi Abgrall. An extension of Roe's upwind scheme to
algebraic
equilibrium real gas models. Comput.
&
Fluids, 19(2):171--182, 1991.
- Rémi Abgrall, Hypersonic calculations by Riemann solvers
techniques. Comput. Phys. Commun.,
65(1-3):1--7,
1991.
- 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.
- Didier Chargy, Rémi Abgrall, Loula Fézoui, and
Bernard
Larrouturou.Conservative numerical schemes for multicomponent inviscid
flows. Rech. Aérospat.,
(2):61--80,
1992
- Rémi Abgrall. How to prevent pressure oscillations in
multicomponent flow calculations: a quasi-conservative approach. J. Comput. Phys., 125(1):150--160,
1996
- Richard Saurel and Rémi Abgrall. A simple method for
compressible
multifluid flows. SIAM J. Sci.
Comput., 21(3):1115--1145, 1999.
- Richard Saurel and Rémi Abgrall. A multiphase Godunov
method for
compressible multifluid and multiphase flows. J. Comput. Phys., 150(2):425--467,
1999.
- Rémi Abgrall and Smadar Karni. Computations of
compressible
multifluids. J. Comput. Phys.,
169(2):594--623,
2001.
- 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.
- Germain Billet and Rémi Abgrall. An adaptive
shock-capturing
algorithm for solving unsteady reactive flows. Comput.
Fluids,
32(10):1473--1495, 2003.
- 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
- Rémi Abgrall and Richard
Saurel. Discrete equations
for
physical
and numerical compressible multiphase mixtures. J. Comput. Phys., 186(2):361--396,
2003.
- 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).
- 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.
- 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.
- 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
- 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
- Rémi Abgrall. On
essentially non-oscillatory schemes on
unstructured meshes: Analysis and implementation, J. Comput. Phys. , 114(1):45--58,
1994.
- 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.
- 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
- Rémi Abgrall. Numerical discretization of the first-order
Hamilton-Jacobi equation on triangular meshes. Commun. Pure Appl. Math.,
49(12):1339--1373, 1996.
- Steeve Augoula and Rémi Abgrall. High order numerical
discretization for Hamilton-Jacobi equations on triangular
meshes. J. Sci. Comput.,
15(2):197--229,
2000.
- Rémi Abgrall. Numerical
discretization
of
boundary
conditions for
first order Hamilton--Jacobi equations. SIAM J. Numer. Anal.,
41(6):2233--2261, 2003.
- 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
- 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
- Rémi Abgrall and Ami Harten. Multiresolution
representation in
unstructured meshes. SIAM J.
Numer.
Anal., 35(6):2128--2146, 1998.
Shallow
water
equations
- 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
- 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
- Rémi Abgrall. Toward
the
ultimate
conservative scheme:
Following
the quest. J. Comput. Phys.,
167(2):277--315,
2001.
- Rémi Abgrall and Timothy Barth. Residual distribution
schemes for
conservation laws via adaptive quadrature. SIAM J. Sci. Comput.,
24(3):732--769, 2002.
- Rémi Abgrall and Philipp L. Roe, High-order
fluctuation schemes on
triangular meshes. J. Sci.
Comput., 19(1-3):3--36, 2003.
- 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.
- 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.
- 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.
- Rémi Abgrall and Fabien Marpeau. Residual distribution
schemes on
quadrilateral meshes. J.
Scientific Computing, 30(1), 2007
- Rémi Abgrall. Essentially
non
oscillatory
residual
distribution
schemes for hyperbolic problems. J.
Comput.
Phys., 214(2):773--808, 2006.
- Rémi Abgrall. Residual
distribution schemes: current
status and
future trends. Computer and Fluids, 35(7):641--669, 2006.
invited paper
- 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)
- 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
- 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
- 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.
- 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.
- 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.
- 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.
- 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
- 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.
- 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.
- 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
- 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.
- 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.
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- 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.
- 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.
- 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.
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Comptes Rendus de l'Académie des Sciences
- 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.
- 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.
- 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.
- 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.
- 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.
- Mikaël Papin and Rémi Abgrall. Entropic
closure laws for
two-fluid seven equation models. C. R. Acad. Sci.
Mécanique,
333(11):838--842, 2005.
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to top
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- 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
Chapters
of books
- 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.
- 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.
- 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.
- 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.
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- Rémi Abgrall and Frédéric Lafon. ENO schemes
on unstructured
meshes. In Lecture series 1993-04.
von
Karman
Institute, 1993.
- Rémi Abgrall and Mohamed Mezine. Residual distribution
schemes
for steady problems. In von
Kà rman Institute Lecture Series, March 2003.
- 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.
- 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.
- Hermann Deconinck and Rémi Abgrall. Introduction to
residual distribution methods. In CFD--higher order
discretization methods. von
Kà rman
Institute, 2005.
- 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.
- 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.