Séminaire Doctorants
organisé par l'équipe DOCT
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Esteban Coiffier
Numerical staggered conservative scheme for the simulation of low Mach number flows
9 octobre 2025 - 16:30Salle de conférences IRMA
We are interested here in the simulation of compressible fluid mechanics equations in a low Mach
number regime. More specifically, we study the numerical approximation of the barotropic Euler
equations using finite volume/finite element methods.
Low Mach number flows are notoriously difficult to simulate with classical finite volume methods,
mainly because their accuracy depends on the mesh shape [2]. Inspired by the MAC scheme [3]
(introduced for the simulation of incompressible fluids), one of the proposed solutions to address
this issue consists of staggering the velocity degrees of freedom at the mesh faces to improve the
approximation of the divergence operator. The challenge of such a placement of unknowns lies in
defining conservation, compared to colocated finite volume methods where it directly results from the
scheme’s formulation.
In[4],the authors proposed conservative staggered schemes based on Crouzeix-Raviart and Rannacher-
Turek finite elements for each velocity component.
Our approach follows this line of research with the following originality : we introduce a staggered
discretization based on the de Rham complex of Nédélec-Raviart-Thomas finite elements [1]. More
precisely, the velocity is in the Raviart-Thomas space, requiring only one degree of freedom per mesh
face in any spatial dimension.
The interest in relying on a discrete de Rham complex is illustrated through an asymptotic analysis
in the Mach number [5] :
i) The complex allows us to demonstrate the existence of a discrete Hodge decomposition, which
helps identify the low Mach limit of the scheme.
ii) Using this formalism, stabilization terms have been constructed to propagate low Mach number
acoustic waves in explicit time integration.
In this presentation, we will introduce both the theoretical tools that ensure accuracy at low Mach
numbers and the procedure for obtaining a conservative finite volume scheme. We will illustrate the
scheme’s properties through numerical simulations in 2d.
[1] A. Ern, J.-L. Guermond. Theory and practice of finite elements, vol. 159. Springer, 2004.
[2] H. Guillard. On the behavior of upwind schemes in the low mach number limit. iv : P0 approxi-
mation on triangular and tetrahedral cells. Computers & fluids, 38(10), 1969–1972, 2009.
[3] F. H. Harlow. Mac numerical calculation of time-dependent viscous incompressible flow of fluid
with free surface. Phys. Fluid, 8, 12, 1965.
[4] R. Herbin, W. Kheriji, J.-C. Latché. On some implicit and semi-implicit staggered schemes for
the shallow water and euler equations. ESAIM : Mathematical Modelling and Numerical Analysis,
48(6), 1807–1857, 2014.
[5] J. Jung, V. Perrier. Steady low mach number flows : identification of the spurious mode and
filtering method. Journal of Computational Physics, 468, 111462, 2022. -
Christopher Nicol
27 lignes sur une surface cubique
16 octobre 2025 - 16:30Salle de conférences IRMA
De tout temps, les doctorants se sont confrontés à la gêne de devoir expliquer à des invités la signification des moules en plâtre du salon de l'IRMA. Ayant chanté face à la géométrie algébrique, ces cigales se trouvent fort dépourvues et en viennent à demander l'aide de l'équipe AGA. Partageuse, la fourmi expliquera donc la géométrie des surfaces cubiques complexes, et notamment la présence de 27 lignes sur celle-ci, fournissant un aperçu des variétés de Fano des lignes. À l'issue, la cigale sera autonome pour décrire la décoration du salon à des invités extérieurs lors d'un événement futur (RJMI, fête des sciences, pot de thèse). -
Victor Le Guilloux
TBA
23 octobre 2025 - 16:30Salle de conférences IRMA