Asymptotic preserving schemes for linear transport on unstructured meshes

Asymptotic preserving schemes for hyperbolic heat equation on unstructured meshes

Key words : Hyperbolic heat equation, unstructured meshes, finite volume methods, nodal scheme, AP schemes, hyperbolic system with source terms.
Proceedings : An asymptotic preserving scheme for P1 model using classical diffusion schemes on unstructured polygonal meshes, E. Franck, P. Hoch, P. Navaro and G. Samba, ESAIM: PROCEEDINGS, October 2011, Vol. 32, p. 56-75.
Proceedings : A priori analysis of asymptotic preserving schemes with the modified equation. B. Després (principal autor), C. Buet et E. Franck. Hyperbolic problems: theory, numerics and applications, AIMS on Applied Mathematics,vol 8, pp 501.
Paper : Design of asymptotic preserving finite volume schemes for hyperbolic heat equation on unstructured meshes , C. Buet, B. Després, E. Franck, Numerische Mathematik, October 2012, Volume 122, Issue 2, pp 227-278.
Paper : Proof of uniform convergence for a cell-centered AP discretization of the hyperbolic heat equation on general meshes , C. Buet, B. Després, E. Franck, T. Leroy, Mathematics of computation, 12 Septembre 2016.

Asymptotic preserving schemes for Friedrichs systems and linear transport

Key words : Friedrichs system, discrete ordinate method, spherical harmonics expansion, unstructured meshes, finite volume methods, nodal scheme, AP schemes, hyperbolic system with source terms, micro-macro decomposition.
Paper : Asymptotic preserving schemes for Friedrichs systems with stiff relaxation on unstructured meshes: applications to the angular discretization models in linear transport, C. Buet, B. Després, E. Franck, Journal Scientific Computing.

Asymptotic preserving scheme with maximum principle for non linear hyperbolic model in radiative transfer

Key words : radiative transfer, unstructured meshes, finite volume methods, non linear moments model, AP schemes, entropy, maximum principle.
Proceedings : Asymptotic Preserving Finite Volumes Discretization For Non-Linear Moment Model On Unstructured Meshes, C. Buet, B. Després, E. Franck, Finite Volumes for Complex Applications VI Problems and Perspectives, Springer Proceedings in Mathematics Volume 4, 2011, pp 467-474.
Paper : An asymptotic preserving scheme with the maximum principle for the M1 model on distorted meshes, C. Buet, B. Després, E. Franck, Comptes Rendus Mathematique, Volume 350, Issues 11-12, June 2012, Pages 633-638.

Asymptotic preserving and Well-Balanced schemes for non linear hyperbolic systems in fluid mechanics

Asymptotic preserving schemes for Euler with friction and gravity

Key words : Euler equations, unstructured meshes, finite volume methods, AP schemes, entropy, well-balanced methods, Lagrange+remap scheme.
Proceedings : Modified Finite Volume Nodal Scheme for Euler Equations with Gravity and Friction, E. Franck, Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects Springer Proceedings in Mathematics & Statistics Volume 77, 2014, pp 285-292.

Scheme for lienar acoustic. Application to low-mach flows

Preprint : Modified finite volume scheme with local high order discretization of hydrostatic equilibrium for Euler equations with external forces, E. Franck, L. Mendoza

Time schemes for the reduced MHD equations

EUROfusion project research (2014): JOREK, BOUT++ non-linear MHD modelling of MHD instabilities and their control in existing tokamaks and ITER, Becoulet M. (PI), Orain F., Dif-Pradalier G., Latu G., Grandgirard V., Passeron C., Morales J., Nkonga B., Galligo A., Guillard H., Mourrain B., Ratnani A., Futatani S., Ramet P., Lacoste X., Hoelzl M., Sonnendruecker E., Strumberger E., Franck E., Tichmann C., Pamela S., Wilson H., Dudson B., Imada K., Westerhof E., Pavel C., Lessig A.
EUROfusion Enabling Research Project (2015-2017): Global non-linear MHD modeling in toroidal geometry of disruptions, edge localized modes, and techniques for their mitigation and suppression. Hoelzl M. (PI),Becoulet M., Sonnendruecker E., Strumberger E., Pautasso G., Ratnani A., Orain F., Nardon E., Dif-Pradalier G., Latu G., Grandgirard V., Passeron C., Morales J., Nkonga B., Guillard H., Sangam A., Franck E., Pamela S., Cahyna P., Seidl J., Futatani S., Westerhof E.
Key words : nonlinear time schemes, preconditioning, stability, multiscale problems, reduced MHD, plasma physics, Jorek code
Preprint : Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code, E. Franck, M. Hölzl, A. Lessig, E. Sonnendrücker.