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# Recent publications of Philippe Angot

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.

### Journal articles25 documents

• Mohamed Kara, Salim Mesbahi, Philippe Angot. The Fictitious Domain Method with Sharp Interface for Elasticity Systems with General Jump Embedded Boundary Conditions. Advances in Applied Mathematics and Mechanics, Global Science Press, 2021, 13 (1), pp.119--139. ⟨10.4208/aamm.OA-2019-0119⟩. ⟨hal-02915666⟩
• Philippe Angot, Benoît Goyeau, J Ochoa-Tapia. A nonlinear asymptotic model for the inertial flow at a fluid-porous interface. Advances in Water Resources, Elsevier, 2021, 149, ⟨10.1016/j.advwatres.2020.103798⟩. ⟨hal-02982802v2⟩
• Arthur Sarthou, Stéphane Vincent, Philippe Angot, Jean-Paul Caltagirone. The Algebraic Immersed Interface and Boundary Method for Elliptic Equations with Jump Conditions. Open Journal of fluid Dynamics, Scientific Research, 2020, 10 (3), pp.239 - 269. ⟨10.4236/ojfd.2020.103015⟩. ⟨hal-02921726⟩
• Philippe Angot, Rima Cheaytou. Vector penalty-projection methods for open boundary conditions with optimal second-order accuracy. Communications in Computational Physics, Global Science Press, 2019, 26 (4), pp.1008--1038. ⟨10.4208/cicp.OA-2018-0016⟩. ⟨hal-01198400v3⟩
• Philippe Angot, Rima Cheaytou. On the error estimates of the vector penalty-projection methods: Second-order scheme. Mathematics of Computation, American Mathematical Society, 2018, 87 (313), pp.2159--2187. ⟨10.1090/mcom/3309⟩. ⟨hal-01632234⟩
• Philippe Angot. WELL-POSED STOKES/BRINKMAN AND STOKES/DARCY COUPLING REVISITED WITH NEW JUMP INTERFACE CONDITIONS. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2018, 52 (5), pp.1875--1911. ⟨10.1051/m2an/2017060⟩. ⟨hal-01635289⟩
• Philippe Angot, Benoît Goyeau, J. Alberto Ochoa-Tapia. Asymptotic modeling of transport phenomena at the interface between a fluid and a porous layer: Jump conditions. Physical Review E , American Physical Society (APS), 2017, 95 (6), ⟨10.1103/PhysRevE.95.063302⟩. ⟨hal-01583856⟩
• Philippe Angot, Zhilin Li. AN AUGMENTED IIM & PRECONDITIONING TECHNIQUE FOR JUMP EMBEDDED BOUNDARY CONDITIONS. International Journal of Numerical Analysis and Modeling, Institute for Scientific Computing and Information, 2017, 14 (4-5), pp.712-729. ⟨hal-01632229⟩
• Philippe Angot, Jean-Paul Caltagirone, Pierre Fabrie. A kinematic vector penalty-projection method for incompressible flow with variable density. Comptes Rendus Mathématique, Elsevier Masson, 2016, Ser. I, 354 (11), pp.1124--1131. ⟨10.1016/j.crma.2016.06.007⟩. ⟨hal-01378046⟩
• Philippe Angot, Gilles Carbou, Victor Péron. Asymptotic study for Stokes-Brinkman model with jump embedded transmission conditions. Asymptotic Analysis, IOS Press, 2016, 96 (3-4), pp.223-249. ⟨10.3233/ASY-151336⟩. ⟨hal-01184429⟩
• Philippe Angot, Thomas Auphan, Olivier Guès. An optimal penalty method for a hyperbolic system modeling the edge plasma transport in a tokamak. Journal of Computational Physics, Elsevier, 2014, 261, pp.1 - 22. ⟨10.1016/j.jcp.2013.12.037⟩. ⟨hal-00955267⟩
• Philippe Angot, Jean-Paul Caltagirone, Pierre Fabrie. Fast discrete Helmholtz-Hodge decompositions in bounded domains. Applied Mathematics Letters, Elsevier, 2013, 26 (4), pp.445--451. ⟨10.1016/j.aml.2012.11.006⟩. ⟨hal-00756959⟩
• Benjamin Kadoch, Dmitry Kolomenskiy, Philippe Angot, Kai Schneider. A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles. Journal of Computational Physics, Elsevier, 2012, 231 (12), pp.4365-4383. ⟨10.1016/j.jcp.2012.01.036⟩. ⟨hal-01032208⟩
• Philippe Angot, Johnwill Keating, Peter D. Minev, Peter Minev. A direction splitting algorithm for incompressible flow in complex geometries. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2012, 217-220, pp.111 - 120. ⟨10.1016/j.cma.2012.01.011⟩. ⟨hal-01632281⟩
• Philippe Angot, Jean-Paul Caltagirone, Pierre Fabrie. A fast vector penalty-projection method for incompressible non-homogeneous or multiphase Navier-Stokes problems. Applied Mathematics Letters, Elsevier, 2012, 25 (11), pp.1681--1688. ⟨10.1016/j.aml.2012.01.037⟩. ⟨hal-00667121⟩
• Philippe Angot, Pierre Fabrie. Convergence results for the vector penalty-projection and two-step artificial compressibility methods. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2012, 17 (5), pp. 1383--1405, communicated by Roger Temam. ⟨10.3934/dcdsb.2012.17.1383⟩. ⟨hal-00653113v2⟩
• Philippe Angot, Jean-Paul Caltagirone, Pierre Fabrie. A new fast method to compute saddle-points in constrained optimization and applications. Applied Mathematics Letters, Elsevier, 2012, 25 (3), pp.245-251. ⟨10.1016/j.aml.2011.08.015⟩. ⟨hal-00626163⟩
• Philippe Angot. On the well-posed coupling between free fluid and porous viscous flows. Applied Mathematics Letters, Elsevier, 2011, 24 (6), pp.803-810. ⟨10.1016/j.aml.2010.07.008⟩. ⟨hal-00476386v2⟩
• Philippe Angot. A fictitious domain model for the Stokes/Brinkman problem with jump embedded boundary conditions. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2010, 348 (11-12), pp.697-702. ⟨hal-00476369⟩
• Philippe Angot, Franck Boyer, Florence Hubert. Asymptotic and numerical modelling of flows in fractured porous media. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2009, 23 (2), pp.239--275. ⟨hal-00127023v2⟩
• Pascal Poullet, Jacques Laminie, Philippe Angot, Carine Févrière. On the penalty-projection method for the Navier-Stokes equations with the MAC mesh. Journal of Computational and Applied Mathematics, Elsevier, 2009, 226, pp.228-245. ⟨10.1016/j.cam.2008.08.014⟩. ⟨hal-00530820⟩
• Philippe Angot, Matthieu Jobelin, Jean-Claude Latché. Error analysis of the Penalty-Projection method for the time dependent Stokes equations. International Journal on Finite Volumes, Institut de Mathématiques de Marseille, AMU, 2009, 6 (1), pp.1-26. ⟨hal-00482143⟩
• Pascal Poullet, Carine Févrière, Philippe Angot. A penalty-projection method using staggered grids for incompressible flows. Lecture Notes in Computer Science, Springer, 2008, 4818, pp.192-200. ⟨hal-00530822⟩
• Isabelle Ramière, Philippe Angot, Michel Belliard. A Fictitious domain approach with spread interface for elliptic problems with general boundary conditions. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2007, 196 (4-6), pp 766-781. ⟨hal-00274445⟩
• Isabelle Ramière, Philippe Angot, Michel Belliard. A general fictitious domain method with immersed jumps and multilevel nested structured meshes. Journal of Computational Physics, Elsevier, 2007, 225 (2), pp 1347-1387. ⟨10.1016/j.jcp.2007.01.026⟩. ⟨hal-00274475⟩

### Conference papers13 documents

• Philippe Angot, Jean-Paul Caltagirone, Pierre Fabrie. A spectacular solver of low-Mach multiphase Navier-Stokes problems under strong stresses. 4th International Conference on Turbulence and Interactions, Institut d'Etudes Scientifiques de Cargèse & ONERA, Nov 2015, Cargèse (Corsica), France. ⟨hal-01248744⟩
• Philippe Angot, Thomas Auphan, Olivier Guès. Asymptotic-preserving methods for an anisotropic model of electrical potential in a tokamak. 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⟩. ⟨hal-01018388⟩
• Philippe Angot, Rima Cheaytou. VECTOR PENALTY-PROJECTION METHOD FOR INCOMPRESSIBLE FLUID FLOWS WITH OPEN BOUNDARY CONDITIONS. Algoritmy 2012, 19th Conference on Scientific Computing, Sep 2012, Vysoké Tatry, Podbanské (Slovakia), Slovakia. pp.219--229. ⟨hal-00752503⟩
• Kaï Schneider, Benjamin Kadoch, Dmitry Kolomenskiy, Philippe Angot. A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles. 64th Annual Conference, Division of Fluid Dynamics, American Physical Society, Nov 2011, Baltimore, United States. ⟨10.1016/j.jcp.2012.01.036⟩. ⟨hal-01307209⟩
• Philippe Angot, Jean-Paul Caltagirone, Pierre Fabrie. A Spectacular Vector Penalty-Projection Method for Darcy and Navier-Stokes Problems. International Symposium FVCA6, Jun 2011, Prague, Czech Republic. pp.39-47. ⟨hal-00610690⟩
• Philippe Angot, Thomas Auphan, Olivier Guès. Penalty Methods for the Hyperbolic System Modelling the Wall-Plasma Interaction in a Tokamak. International Symposium FVCA6, Jun 2011, Prague, Czech Republic. pp.31-38. ⟨hal-00627313⟩
• Philippe Angot. Well-posed Stokes/Brinkman and Stokes/Darcy problems for coupled fluid-porous viscous flows. 8th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2010), Sep 2010, Rhodes, Greece. pp.2208-2211, ⟨10.1063/1.3498412⟩. ⟨hal-00610713⟩
• Arthur Sarthou, Stéphane Vincent, Philippe Angot, Jean-Paul Caltagirone. The Sub-Mesh Penalty Method. 5th International Symposium on Finite Volumes for Complex Applications, Jun 2008, Aussois, France. pp.633. ⟨hal-00390080⟩
• Philippe Angot, Jean-Paul Caltagirone, Pierre Fabrie. Vector penalty-projection methods for the solution of unsteady incompressible flows. 5th International Symposium on Finite Volumes for Complex Applications, Jun 2008, Aussois, France. pp.169-176. ⟨hal-00483583⟩
• Pascal Poullet, Carine Févrière, Philippe Angot, Jacques Laminie. An accurate projection method for incompressible flows. 15th Meeting of the Caribbean Academy of Science, May 2006, Gosier, Guadeloupe. ⟨hal-00778158⟩
• Carine Févrière, Philippe Angot, Pascal Poullet. An accurate projection method using staggered grids for incompressible flows. CMAIA 2006, a Conference on Mathematics and its Applications, Sep 2006, St Augustine, Trinidad and Tobago. ⟨hal-00770273⟩
• Isabelle Ramière, Philippe Angot, Michel Belliard. Fictitious domain methods to solve convection-diffusion problems with general boundary conditions. Proc. in the 17th Computational Fluid Dynamics Conference AIAA, Jun 2005, Toronto, Canada. Session : "Numerical methods and code optimization I". ⟨hal-00274448⟩
• Isabelle Ramière, Michel Belliard, Philippe Angot. On the simulation of Nuclear Power Plant Components using a fictitious domain approach. NURETH-11, Oct 2005, Avignon, France. paper: 193. ⟨hal-01053745⟩

### Book sections1 document

• Jean-Paul Caltagirone, Philippe Angot. Fluid-Structure Interactions in Discrete Mechanics. 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⟩. ⟨hal-02970449⟩

### Preprints, Working Papers, ...5 documents

• Philippe Angot. Solvability of the variable-viscosity fluid-porous flows coupled with an optimal stress jump interface condition. 2021. ⟨hal-03172378⟩
• Philippe Angot. EARLY ESTIMATIONS OF THE IMPACT OF GENERAL LOCKDOWN TO CONTROL THE COVID-19 EPIDEMIC IN FRANCE. 2020. ⟨hal-02545893⟩
• Philippe Angot. On the unsteady Stokes problem with a nonlinear open artificial boundary condition modelling a singular load. 2013. ⟨hal-00820404⟩
• Arthur Sarthou, Stéphane Vincent, Philippe Angot, Jean-Paul Caltagirone. The algebraic immersed interface and boundary method for elliptic equations with jump conditions. 2009. ⟨hal-00390075v3⟩
• Arthur Sarthou, Stéphane Vincent, Jean-Paul Caltagirone, Philippe Angot. A global procedure for flow and heat transfer simulation with complex obstacles on curvilinear grids. 2008. ⟨hal-00405273⟩