5 papers
Well-Balanced Schemes for Hyperbolic Kinetic Relaxation
León Ãvila, Manuel Castro, Victor Michel-Dansac +1
This work presents a novel family of well-balanced numerical schemes for hyperbolic systems of balance laws based on the kinetic relaxation approach. The method begins by transform…
Towards a fully well-balanced and entropy-stable scheme for the Euler equations with gravity: General equations of state
Victor Michel-Dansac, Andrea Thomann
The present work concerns the derivation of a fully well-balanced Godunov-type finite volume scheme for the Euler equations with a gravitational potential based on an approximate R…
Towards a fully well-balanced and entropy-stable scheme for the Euler equations with gravity: preserving isentropic steady solutions
Christophe Berthon, Victor Michel-Dansac, Andrea Thomann
The present work concerns the derivation of a numerical scheme to approximate weak solutions of the Euler equations with a gravitational source term. The designed scheme is proved…
TVD-MOOD schemes based on implicit-explicit time integration
Victor Michel-Dansac, Andrea Thomann
The context of this work is the development of first order total variation diminishing (TVD) implicit-explicit (IMEX) Runge-Kutta (RK) schemes as a basis of a Multidimensional Opti…
A fully well-balanced hydrodynamic reconstruction
Christophe Berthon, Victor Michel-Dansac
The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady…