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Philippe Angot

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**Five selected articles as the most significative ones** 1. **Philippe Angot**: Analysis of singular perturbations on the Brinkman problem for fictitious domain models of viscous flows, Math. Meth. Appl. Sci. **22**(16), 1395--1412, 1999.This work studies the asymptotic behaviours of the generalized Darcy-Brinkman equation with variable effective porosity and permeability to model incompressible viscous flows in complex fluid-porous-solid systems within volume penalty and fictitious domain methods. These original techniques were early proposed in *Angot and Caltagirone (WCCM2, 1990)*. For fluid-porous systems with an infinite permeability in the pure fluid, the resulting error estimate is optimal with respect to the penalization parameter. For fluid-solid systems, both the $L^{2}$ and $H^{1}$ volume penalty method are investigated with a permeability going to zero in the solid region and/or an effective viscosity going to infinite in the solid obstacle. The latter can be used to penalize the strain rate tensor to get the rigidity of a solid particle transported in the flow. An optimal error estimate is obtained for the $H^{1}$ volume penalty method. Moreover, a simple estimate of the resulting force applied to the solid obstacle is provided. These results are generalized in *Angot et al. (1999)* for the unsteady inertial flows with the Navier-Stokes/Brinkman equations. The numerical validation of this fictitious domain approach is carried out in *Khadra et al. (2000)* for isothermal or convective heat transfer flow problems with non body-fitted obstacles. Moreover, the volume penalty method is extended for hyperbolic systems of conservation laws in *Angot et al. (2014)*. Due to their simplicity, these techniques that have now become standard, are widely used in Computational Fluid Dynamics and incorporated in many numerical simulation codes including commercial software. 2. **Philippe Angot, Franck Boyer and Florence Hubert**: Asymptotic and numerical modelling of flows in fractured porous media, ESAIM: Math. Model. Numer. Anal. **43**(2), 239--275, 2009.This paper follows the ideas proposed in *Angot (2003)* and *Angot et al. (FVCA4, 2005)* to derive dimensionally-reduced models by asymptotic modelling for the flows in fractured porous media. The developed models are shown to be well-posed. Moreover, an original finite volume method is detailed for the numerical solution and the convergence of this scheme is proved. Several numerical validations are provided including benchmark problems. Up to our knowledge, this study is the first in the literature considering fully immersed fractures in the porous media. This topic is now the subject of intense research activity because of its numerous applications to real-world problems. 3. **Philippe Angot, Jean-Paul Caltagirone and Pierre Fabrie**: A fast vector penalty-projection method for incompressible non-homogeneous or multiphase Navier-Stokes problems, Appl. Math. Lett. **25**(11), 1681--1688, 2012. This paper details and validates an original time-splitting scheme, the so-called vector penalty-projection method, briefly proposed in *Angot et al. (FVCA6, 2011)* for the numerical solution of variable-density or multiphase Navier-Stokes equations with strong stresses. This is an efficient alternative to the well-known Chorin-Temam projection method with a scalar pressure correction made by the solution of a Poisson equation. The method is based on new fast discrete Helmholtz-Hodge decompositions in bounded domains studied in *Angot et al. (2013)*. Unlike all scalar projection methods, the vector projection method is shown to be fast and accurate for multiphase flows with large density (up to $10^{6}$) or viscosity (up to $10^{17}$) ratios, as demonstrated in the benchmark problem of free fall of an heavy ball. In a more recent paper *Angot et al. (2016)*, an original kinematic version of this method is proposed. Unlike to usual methods which fail for density ratios of several hundreds, our method remains stable and accurate for multiphase flow benchmark problems of bubble dynamics (with surface tension) with a density ratio up to $10^{4}$ (for air bubles in a liquid melted steel). Moreover, there is no spurious eddies up to machine precision close to the interface between the fluid phases that is one of the common drawbacks of all numerical methods in this topic. In *Angot and Cheaytou (2019)*, the vector penalty-projection method is also shown to be fast and accurate for open boundary conditions. Indeed, the optimal second-order precision is fully recovered unlike to usual time-splitting schemes. 4. **Philippe Angot**: Well-posed Stokes/Brinkman and Stokes/Darcy coupling revisited with new jump interface conditions, ESAIM: Math. Model. Numer. Anal. **52**(5), 1875--1911, 2018.This work proves the global solvability in time of the unsteady Stokes/Brinkman and Stokes/Darcy coupled problems with no restriction on the size of the data for the macroscale modelling of viscous flows in fluid-porous systems. The work follows the ideas and the mathematical framework briefly proposed for the steady problems in *Angot (2010, 2011)* to deal with jump interface conditions of both the tangential velocity and stress vectors. The new jump interface conditions considered here are theoretically derived in *Angot et al. (2017)* for the non-inertial fluid-porous flow using the volume averaging method and a suitable asymptotic analysis. Moreover, they are shown to be physically relevant for arbitrary flow directions and they are inherently able to take account of anisotropic effects unlike *ad-hoc* extended Beavers-Joseph interface conditions that are most often used in the literature. In particular, the well-posedness is proved whatever the size of the slip coefficient $\\alpha\\geq0$ for the full Beavers-Joseph jump condition. The previous results only proved the solvability either for the approximate and simplified Beavers-Joseph-Saffman condition (where the effective velocity jump is no more taken into account) or for complete Beavers-Joseph's condition such that $\\alpha^2$ is sufficiently small. 5. **Philippe Angot, Benoît Goyeau and J. Alberto Ochoa-Tapia**: A nonlinear asymptotic model for the inertial flow at a fluid-porous interface, Adv. Water Res. **149**, 103798, 2021 (online 30 October 2020).In this theoretical study of mathematical modelling, we develop an asymptotic analysis of the homogenized Navier-Stokes equations in the thin transition porous layer between the pure fluid and the homogeneous porous medium. This yields an original nonlinear and multi-dimensional interface model for the macroscale inertial flow over a permeable medium. These new jump interface conditions that inherently include the anisotropic effects are shown to be physically meaningful for arbitrary inertial flow directions. The present theory also enables us to analyze the dependence on porosity of the slip and friction coefficients included in the proposed jump interface conditions. Moreover, the coupled Navier-Stokes/Darcy-Forchheimer fluid-porous model supplemented with the present set of interface conditions is shown to be globally dissipative. This is the first nonlinear and multi-dimensional globally dissipative model proposed in the literature for the inertial flow at a permeable interface with arbitrary flow directions.

Publications

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Necessary and sufficient Tauberian condition for both Cesàro and Abel summability

Philippe Angot
Jahresbericht der Deutschen Mathematiker-Vereinigung, inPress, ⟨10.1365/s13291-024-00279-1⟩
Journal articles hal-04227761v4
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Momentum transport in the free fluid-porous medium transition layer: the one-domain approach

Roel Hernandez-Rodriguez , Philippe Angot , Benoit Goyeau , J. Alberto Ochoa-Tapia
Chemical Engineering Science, 2022, 248 (Part A), pp.117111. ⟨10.1016/j.ces.2021.117111⟩
Journal articles hal-03351185v1
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The Fictitious Domain Method with Sharp Interface for Elasticity Systems with General Jump Embedded Boundary Conditions

Mohamed Kara , Salim Mesbahi , Philippe Angot
Advances in Applied Mathematics and Mechanics, 2021, 13 (1), pp.119--139. ⟨10.4208/aamm.OA-2019-0119⟩
Journal articles hal-02915666v1
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A nonlinear asymptotic model for the inertial flow at a fluid-porous interface

Philippe Angot , Benoît Goyeau , J Alberto Ochoa-Tapia
Advances in Water Resources, 2021, 149, ⟨10.1016/j.advwatres.2020.103798⟩
Journal articles hal-02982802v2
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The Algebraic Immersed Interface and Boundary Method for Elliptic Equations with Jump Conditions

Arthur Sarthou , Stéphane Vincent , Philippe Angot , Jean-Paul Caltagirone
Open Journal of fluid Dynamics, 2020, 10 (3), pp.239 - 269. ⟨10.4236/ojfd.2020.103015⟩
Journal articles hal-02921726v1
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Vector penalty-projection methods for open boundary conditions with optimal second-order accuracy

Philippe Angot , Rima Cheaytou
Communications in Computational Physics, 2019, 26 (4), pp.1008--1038. ⟨10.4208/cicp.OA-2018-0016⟩
Journal articles hal-01198400v3
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On the error estimates of the vector penalty-projection methods: Second-order scheme

Philippe Angot , Rima Cheaytou
Mathematics of Computation, 2018, 87 (313), pp.2159--2187. ⟨10.1090/mcom/3309⟩
Journal articles hal-01632234v1
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WELL-POSED STOKES/BRINKMAN AND STOKES/DARCY COUPLING REVISITED WITH NEW JUMP INTERFACE CONDITIONS

Philippe Angot
ESAIM: Mathematical Modelling and Numerical Analysis, 2018, 52 (5), pp.1875--1911. ⟨10.1051/m2an/2017060⟩
Journal articles hal-01635289v1
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AN AUGMENTED IIM & PRECONDITIONING TECHNIQUE FOR JUMP EMBEDDED BOUNDARY CONDITIONS

Philippe Angot , Zhilin Li
International Journal of Numerical Analysis and Modeling, 2017, 14 (4-5), pp.712-729
Journal articles hal-01632229v1

Asymptotic modeling of transport phenomena at the interface between a fluid and a porous layer: Jump conditions

Philippe Angot , Benoît Goyeau , J. Alberto Ochoa-Tapia
Physical Review E , 2017, 95 (6), ⟨10.1103/PhysRevE.95.063302⟩
Journal articles hal-01583856v1
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Asymptotic study for Stokes-Brinkman model with jump embedded transmission conditions

Philippe Angot , Gilles Carbou , Victor Péron
Asymptotic Analysis, 2016, 96 (3-4), pp.223-249. ⟨10.3233/ASY-151336⟩
Journal articles hal-01184429v1
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A kinematic vector penalty-projection method for incompressible flow with variable density

Philippe Angot , Jean-Paul Caltagirone , Pierre Fabrie
Comptes Rendus. Mathématique, 2016, Ser. I, 354 (11), pp.1124--1131. ⟨10.1016/j.crma.2016.06.007⟩
Journal articles hal-01378046v1
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An optimal penalty method for a hyperbolic system modeling the edge plasma transport in a tokamak

Philippe Angot , Thomas Auphan , Olivier Guès
Journal of Computational Physics, 2014, 261, pp.1 - 22. ⟨10.1016/j.jcp.2013.12.037⟩
Journal articles hal-00955267v1
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Fast discrete Helmholtz-Hodge decompositions in bounded domains

Philippe Angot , Jean-Paul Caltagirone , Pierre Fabrie
Applied Mathematics Letters, 2013, 26 (4), pp.445--451. ⟨10.1016/j.aml.2012.11.006⟩
Journal articles hal-00756959v1
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A fast vector penalty-projection method for incompressible non-homogeneous or multiphase Navier-Stokes problems

Philippe Angot , Jean-Paul Caltagirone , Pierre Fabrie
Applied Mathematics Letters, 2012, 25 (11), pp.1681--1688. ⟨10.1016/j.aml.2012.01.037⟩
Journal articles hal-00667121v1
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Convergence results for the vector penalty-projection and two-step artificial compressibility methods

Philippe Angot , Pierre Fabrie
Discrete and Continuous Dynamical Systems - Series B, 2012, 17 (5), pp. 1383--1405, communicated by Roger Temam. ⟨10.3934/dcdsb.2012.17.1383⟩
Journal articles hal-00653113v2

A direction splitting algorithm for incompressible flow in complex geometries

Philippe Angot , Johnwill Keating , Peter D. Minev , Peter D Minev
Computer Methods in Applied Mechanics and Engineering, 2012, 217-220, pp.111 - 120. ⟨10.1016/j.cma.2012.01.011⟩
Journal articles hal-01632281v1
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A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles

Benjamin Kadoch , Dmitry Kolomenskiy , Philippe Angot , Kai Schneider
Journal of Computational Physics, 2012, 231 (12), pp.4365-4383. ⟨10.1016/j.jcp.2012.01.036⟩
Journal articles hal-01032208v1
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A new fast method to compute saddle-points in constrained optimization and applications

Philippe Angot , Jean-Paul Caltagirone , Pierre Fabrie
Applied Mathematics Letters, 2012, 25 (3), pp.245-251. ⟨10.1016/j.aml.2011.08.015⟩
Journal articles hal-00626163v1
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On the well-posed coupling between free fluid and porous viscous flows

Philippe Angot
Applied Mathematics Letters, 2011, 24 (6), pp.803-810. ⟨10.1016/j.aml.2010.07.008⟩
Journal articles hal-00476386v2
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A fictitious domain model for the Stokes/Brinkman problem with jump embedded boundary conditions

Philippe Angot
Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2010, 348 (11-12), pp.697-702
Journal articles hal-00476369v1
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Asymptotic and numerical modelling of flows in fractured porous media

Philippe Angot , Franck Boyer , Florence Hubert
ESAIM: Mathematical Modelling and Numerical Analysis, 2009, 23 (2), pp.239--275
Journal articles hal-00127023v2
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Error analysis of the Penalty-Projection method for the time dependent Stokes equations

Philippe Angot , Matthieu Jobelin , Jean-Claude Latché
International Journal on Finite Volumes, 2009, 6 (1), pp.1-26
Journal articles hal-00482143v1

On the penalty-projection method for the Navier-Stokes equations with the MAC mesh

Pascal Poullet , Jacques Laminie , Philippe Angot , Carine Févrière
Journal of Computational and Applied Mathematics, 2009, 226, pp.228-245. ⟨10.1016/j.cam.2008.08.014⟩
Journal articles hal-00530820v1

A penalty-projection method using staggered grids for incompressible flows

Pascal Poullet , Carine Févrière , Philippe Angot
Lecture Notes in Computer Science, 2008, 4818, pp.192-200
Journal articles hal-00530822v1
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A Fictitious domain approach with spread interface for elliptic problems with general boundary conditions

Isabelle Ramière , Philippe Angot , Michel Belliard
Computer Methods in Applied Mechanics and Engineering, 2007, 196 (4-6), pp 766-781
Journal articles hal-00274445v1
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A general fictitious domain method with immersed jumps and multilevel nested structured meshes

Isabelle Ramière , Philippe Angot , Michel Belliard
Journal of Computational Physics, 2007, 225 (2), pp 1347-1387. ⟨10.1016/j.jcp.2007.01.026⟩
Journal articles hal-00274475v1
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Numerical computation of Navier-Stokes two-phase flows

Philippe Angot
Mathematical Fluid Dynamics -- Advanced Summer School, Aug 2021, Cargèse (Institut d'Etudes Scientifiques), Corsica, France
Conference papers hal-03356887v1
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Simulation of a particulate flow in 3D using volume penalization methods

Philippe Angot , Batteux Léa , Jacques Laminie , Pascal Poullet
Turbulence and Interactions -Proceedings of the TI 2018 conference, Jun 2018, Trois-Îlets, Martinique
Conference papers hal-03089392v1
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Asymptotic modelling of multi-dimensional jump boundary conditions at a fluid-porous interface

Philippe Angot , Benoît Goyeau , J. Alberto Ochoa-Tapia
13èmes Journéess d'études des Milieux Poreux 2016, Oct 2016, Anglet, France
Conference papers hal-01394516v1
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A spectacular solver of low-Mach multiphase Navier-Stokes problems under strong stresses

Philippe Angot , Jean-Paul Caltagirone , Pierre Fabrie
4th International Conference on Turbulence and Interactions, Institut d'Etudes Scientifiques de Cargèse & ONERA, Nov 2015, Cargèse (Corsica), France
Conference papers hal-01248744v1
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Asymptotic-preserving methods for an anisotropic model of electrical potential in a tokamak

Philippe Angot , Thomas Auphan , Olivier Guès
International Symposium of Finite Volumes for Complex Applications VII (FVCA7), Jun 2014, Berlin, Germany. pp.471-478, ⟨10.1007/978-3-319-05591-6_46⟩
Conference papers hal-01018388v1
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VECTOR PENALTY-PROJECTION METHOD FOR INCOMPRESSIBLE FLUID FLOWS WITH OPEN BOUNDARY CONDITIONS

Philippe Angot , Rima Cheaytou
Algoritmy 2012, 19th Conference on Scientific Computing, Sep 2012, Vysoké Tatry, Podbanské (Slovakia), Slovakia. pp.219--229
Conference papers hal-00752503v1
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Penalty Methods for the Hyperbolic System Modelling the Wall-Plasma Interaction in a Tokamak

Philippe Angot , Thomas Auphan , Olivier Guès
International Symposium FVCA6, Jun 2011, Prague, Czech Republic. pp.31-38
Conference papers hal-00627313v1
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A Spectacular Vector Penalty-Projection Method for Darcy and Navier-Stokes Problems

Philippe Angot , Jean-Paul Caltagirone , Pierre Fabrie
International Symposium FVCA6, Jun 2011, Prague, Czech Republic. pp.39-47
Conference papers hal-00610690v1

A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles

Kaï Schneider , Benjamin Kadoch , Dmitry Kolomenskiy , Philippe Angot
64th Annual Conference, Division of Fluid Dynamics, American Physical Society, Nov 2011, Baltimore, United States. ⟨10.1016/j.jcp.2012.01.036⟩
Conference papers hal-01307209v1
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Well-posed Stokes/Brinkman and Stokes/Darcy problems for coupled fluid-porous viscous flows

Philippe Angot
8th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2010), Sep 2010, Rhodes, Greece. pp.2208-2211, ⟨10.1063/1.3498412⟩
Conference papers hal-00610713v1
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The Sub-Mesh Penalty Method

Arthur Sarthou , Stéphane Vincent , Philippe Angot , Jean-Paul Caltagirone
5th International Symposium on Finite Volumes for Complex Applications, Jun 2008, Aussois, France. pp.633
Conference papers hal-00390080v1
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Vector penalty-projection methods for the solution of unsteady incompressible flows

Philippe Angot , Jean-Paul Caltagirone , Pierre Fabrie
5th International Symposium on Finite Volumes for Complex Applications, Jun 2008, Aussois, France. pp.169-176
Conference papers hal-00483583v1

An accurate projection method using staggered grids for incompressible flows

Carine Févrière , Philippe Angot , Pascal Poullet
CMAIA 2006, a Conference on Mathematics and its Applications, Sep 2006, St Augustine, Trinidad and Tobago
Conference papers hal-00770273v1

An accurate projection method for incompressible flows

Pascal Poullet , Carine Févrière , Philippe Angot , Jacques Laminie
15th Meeting of the Caribbean Academy of Science, May 2006, Gosier, Guadeloupe
Conference papers hal-00778158v1
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On the simulation of Nuclear Power Plant Components using a fictitious domain approach

Isabelle Ramière , Michel Belliard , Philippe Angot
NURETH-11, Oct 2005, Avignon, France. paper: 193
Conference papers hal-01053745v1
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Fictitious domain methods to solve convection-diffusion problems with general boundary conditions

Isabelle Ramière , Philippe Angot , Michel Belliard
Proc. in the 17th Computational Fluid Dynamics Conference AIAA, Jun 2005, Toronto, Canada. Session : "Numerical methods and code optimization I"
Conference papers hal-00274448v1
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Fluid-Structure Interactions in Discrete Mechanics

Jean-Paul Caltagirone , Philippe Angot
M. Deville et al. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), 149, Springer International Publishing, pp.3--13, 2021, Turbulence and Interactions -- Proceedings of the TI 2018 Conference, June 25-29, 2018, Les Trois-Îlets, Martinique, France, 978-3-030-65820-5, 978-3-030-65819-9. ⟨10.1007/978-3-030-65820-5_1⟩
Book sections hal-02970449v1