Fran¸ cois Vilar Date and place of birth: 12th of June 1986, Libourne, France Tel.: 06 95 59 45 74, E-mail:
[email protected] Homepage: http://tvilar.pagesperso-orange.fr/ ResearchGate page: http://www.researchgate.net/profile/Francois Vilar
Professional experience Research Engineer, Camille Jordan Institute Scientific computing expert
Mar. 2016 - Today
Development of a parallel simulation platform for the resolution of oceanographic flows, in collaboration with Daniel LeRoux (ICJ) and Thierry Dumont (ICJ), in Claude Bernard University (Lyon). Implementation of a computational code, parallel, based on a discontinuous Galerkin discretization, for the simulation of oceanographic flows. Second-order at first, the code is planned to be extended to higher orders of accuracy. Postdoctoral Research Associate, Brown University Project founded by NASA
Dec. 2013 - Nov. 2015
High-order discontinuous Galerkin and weighted essentially non-oscillatory algorithms for compressible turbulence simulations, project founded by the NASA and supervised by Chi-Wang Shu in Brown University, Rhode Island. Study of a new class of central compact schemes with spectral-like resolution, provided with an inverse Lax-Wendroff inflow boundary condition. An analytical stability analysis has been issued in order to ensure the relevancy of such schemes and boundary condition, and also to design a stable simplification of the inverse Lax-Wendroff procedure. Demonstration of the positivity-preserving property and limitation of high-order entropic stable Summation-By-Parts schemes, work done in collaboration with Mark Carpenter (NASA) and Matteo Parsani (NASA). Analytical proof of the positivity-preserving criterion of a wide class of cell-centered Lagrangian schemes solving gas dynamics equations. The proof has first been carried out for first-order of accuracy, and then has been extended to high-orders, provided a particular limitation ensuring the positivity of the solution at some crucial points inside the cells. In the end, the schemes studied have proved to be extremely robust provided particular slope limitation, for a wide range of equations of state, in 1D and 2D.
Education PhD degree in computational mathematics, Bordeaux I University Defended on the 16th of November 2012
2009 - 2012
High-order discontinuous Galerkin discretization of multi-dimensional Lagrangian hydrodynamics equations, supervised by Pierre-Henri Maire (CEA) and R´ emi Abgrall (Z¨urich Univ.) in the CEA Cesta (Le Barp) research center. 1
Use of high-order discontinuous Galerkin discretization for solving systems of conservation laws, the final goal being the development and implementation of a very high-order cell-centered scheme for the two-dimensional gas dynamics equations written under total Lagrangian formulation, on general unstructured curvilinear grids. In such a formalism, the differential operators being discretized onto the initial coordinates, the fluid flow study is transported from the actual moving mesh to the fixed initial configuration. However, one needs to track the jacobian matrix of the Euler-Lagrange flow map, namely the deformation gradient tensor. Finally, the numerical scheme has to be able to simulate accurately the fluid flow in the frame of extreme physical problems. It also has to allow the mesh to curve in the case of a third-order method, the Euler-Lagrange map and the velocity field being quadratic. Undergraduate degree, MATMECA engineering school Option Mathematics and fluid dynamics
2006 - 2009
ENSEIRB-MATMECA engineering school of the Institut Polytechnique de Bordeaux (IPB), specialized in the modelling and simulation of physical phenomena, resolution of partial differential equations, numerical analysis, solids and fluids mechanics, structure analysis, aerodynamics, parallel programming. Master’s degree, Bordeaux I University Option simulation and Applied Mathematics
2009
Bachelor’s degree, Bordeaux I University Option mathematical engineering
2007
Classes pr´ eparatoires, CpBx of Bordeaux Option Mathematics and Physics
2004 - 2006
Scientific visits Prague University (CVUT), Czech Republic
September, 2010
One-dimensional discontinuous Galerkin type of staggered scheme, collaborative work with Rapha¨el Loub`ere (IMT, CNRS), Pierre-Henri Maire (CEA), Richard Liska (CVUT), Pavel V`achal (CVUT) and Steven Diot (CEA). Resolution of gas dynamics equations in Lagrangian form, with a piecewise constant approximation of the density, the pressure and the internal energy inside the cells, and with a discontinuous Galerkin piecewise polynomial discretization of the velocity in the node-centered cells. Two weeks.
Academic experience 3rd year engineering school internship in applied mathematics
2009
Study of discontinuous Galerkin methods applied to waves propagation problems, supervised by Yoann Ventribout for six months, in the EADS Nucl´etudes research center (Paris). 2nd year engineering school internship in applied mathematics
2008
On bipartite matching and matrix scalings, supervised by Bora U¸car in the team of Iain S. Duff for three months, in the CERFACS laboratory (Toulouse). 2
Teaching Analysis
2010-2011
Second year students of Polytechnicum classes pr´eparatoires - 2nd year university degree (48 hours). Numerical analysis
2009-2010
Second year students of ENSEIRB-MATMECA engineering school - 4th year university degree (4.5 hours). Very high-order numerical schemes for scalar conservation laws
2009-2010
Third year students of ENSEIRB-MATMECA engineering school - 5th year university degree (9 hours).
Areas of expertise Mathematics, scientific computing Implementation and analysis of high-order numerical methods applied to different physical problems such as waves propagation, scalar conservation laws, compressible gas dynamics, or ocean flow dynamics. Parallel programming (MPI and OpenMP), distributed source code management (Git). Physical sciences Compressible and incompressible flows mechanics, aerodynamics, solid mechanics, structure analysis. Programming languages Fortran, Matlab, Mathematica, Maxima. Languages Fluent : French, English. Basic : Spanish.
Conferences USNCCM13
July, 2015
US National congress on computational mechanics, San Diego, USA. Oral presentation on Positivity-preserving two-dimensional cell-centered Lagrangian schemes Website: http://13.usnccm.org/ WCCM XI - ECCM V - ECFD VI
July, 2014
Conference on Computational Methods in Applied Sciences, Barcelona, Spain. Oral presentation on Positivity-preserving cell-centered Lagrangian schemes Website: http://www.wccm-eccm-ecfd2014.org
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MULTIMAT 2013
September, 2013
Conference on Numerical Methods for Multi-Material Fluid Flows, San Francisco, USA. Oral presentation on High-order cell-centered DG scheme for Lagrangian hydrodynamics. Website: https://multimat13.llnl.gov ECCOMAS 2012
September, 2012
Conference on Computational Methods in Applied Sciences, Vienna, Austria. Oral presentation on High-order cell-centered DG scheme for Lagrangian hydrodynamics. Website: http://eccomas2012.conf.tuwien.ac.at/ MULTIMAT 2011
September, 2011
Conference on Numerical Methods for Multi-Material Fluid Flows, Arcachon, France. Oral presentation on Cell-centered DG scheme for Lagrangian hydrodynamics. Website: http://multimat2011.celia.u-bordeaux1.fr/ 4`eme Journ´ ee Calcul Scientifique de Toulouse
June, 2010
Conference on advanced numerical methods and their implementation, Toulouse, France. Presentation of a poster on A DG method for Lagrangian hydrodynamics. Website: http://loubere.free.fr/Calcul Scientifique Toulouse/ ICFD 2010
April, 2010
Conference on Numerical Methods for Fluid Dynamics, Reading, England. Presentation of a poster on A DG method for Lagrangian hydrodynamics. Website: http://www.icfd.rdg.ac.uk/ICFD2010/
Summer schools Erasmus Intensive Program (IP)
July, 2010
Applications of electronics in plasma physics, Rethimno, Crete. Website: http://www.hiper-laser.org/Project News pop-ups/625erasmusintens.html II i-Math School
February, 2010
On numerical solutions of partials differential equations, Malag`a, Spain. Presentation of a poster on A DG method for Lagrangian hydrodynamics. Website: http://www.i-math.org/?q=en/node/1741
Publications [1] F. Vilar, C.-W. Shu and P.-H. Maire, Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: Form first-order to high-orders. Part II: The two-dimensional case. J. of Comp. Phys., 312:416-442, 2016. [2] F. Vilar, C.-W. Shu and P.-H. Maire, Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: Form first-order to high-orders. Part I: The one-dimensional case. J. of Comp. Phys., 312:385-415, 2016. 4
[3] F. Vilar, P.-H. Maire and R. Abgrall, A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total lagrangian formulation on general unstructured grids. J. of Comp. Phys., 276:188-234, 2014. [4] F. Vilar and C.-W. Shu, Development and stability analysis of the inverse LaxWendroff boundary treatment for central compact schemes. ESAIM: Mathematical Modelling and Numerical Analysis, 49(1):39-67, 2014. [5] F. Vilar, Cell-Centered Discontinuous Galerkin discretization for two-dimensional Lagrangian hydrodynamics. Computers and Fluids, 64:64-73, 2012. [6] 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 and Fluids, 46:498-604, 2010.
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