The subcell hydrostatic reconstruction method for Euler equations under gravitational fields with vacuum front
Salle de Séminaires (Orléans)
Salle de Séminaires
This talk solves the Euler equations under gravitational fields based on the subcell hydrostatic reconstruction framework. Different from the other existing schemes, this present one can deal with the vacuum front which can be connected with a polytropic steady state. The method defines the nonconservative product by reconstructing the states on singular layers at every cell interface using the subcell hydrostatic reconstruction method. The reconstruction can maintain the polytropic hydrostatic equilibria even when it is connected with the vacuum front. The scheme's robustness and stability properties, including well-balancing, positivity, and entropy inequality with a positive and bounded production term, are proved. Several numerical experiments illustrate the performance of our method.