Thesis defense


Agnès CHAN will defend her PhD thesis « Innovative numerical schemes for 3D supersonic aerodynamics on unstructured mesh » on November 18th 2022 14h00 (2 pm) at Institut de Mathématiques de Bordeaux  (IMB) in  « Salle de Conference » (Conference Room) building A33

Keywords: Hyperbolic system of conservation laws, Godunov-type scheme, simple approximate Riemann solver, entropy stability, Lagrangian and Eulerian representation, subface-based Finite Volume method.

Advisors:  Raphael Loubère (CNRS) & Pierre-Henri Maire (CEA)

Referees:  Pr. Rémi Abgrall (University of Zurich) & Pr. Claus-Dieter Munz (University of

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A class of cell-centered Finite Volume (FV) schemes has been introduced to discretize the equations of Lagrangian hydrodynamics [1]. The numerical fluxes are evaluated by means of an approximate Riemann solver (RS) located at the grid nodes, which provides the nodal velocity required to move the grid in a compatible manner.


In this thesis, we describe the generalization of this type of discretization to hyperbolic systems of conservation laws written in Eulerian representation [2] on unstructured grid.

The evaluation of the numerical fluxes relies on a nodal solver resulting from a node-based conservation condition.

The construction of this nodal solver uses the Lagrange-to-Eulerian transformation introduced by [3] and revisited in [4] to build positive and entropic Eulerian RS from their Lagrangian counterparts.

The application of this formalism to the case of gas dynamics provides a multidimensional FV scheme which is positive and entropic under an explicit condition on the time step.


An associated FV simulation code has been built in multidimensions for unstructured meshes. Parallelization has been accomplished using the MPI library embedded in PETSc.

A large set of numerical experiments shows that the proposed solver is less sensitive to numerical  instabilities than the classical FV schemes.



  1. Loubère, P.-H. Maire and B. Rebourcet, Handbook of Numerical Methods for Hyperbolic problems, 2016
  2. Gallice, A. Chan , R. Loubère and P.-H. Maire, J. Comp. Phys, 2022
  3. Gallice, Numer. Math., 2003
  4. Chan, G. Gallice, R. Loubère, and P.-H. Maire, Comp. & Fluids, 2021



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