In computational fluid dynamics, low Mach number flows present an  important yet difficult task. These flows live on the border between two  completely different worlds - compressible and incompressible - thus  presenting considerable challenges for numerical methods. Explicit  schemes are typically out of the question while implicit schemes are  very computationally demanding. We will present a class of linearly  implicit schemes for the compressible Euler equations. This class is  based on a linearization of the nonlinear fluxes at a reference state  and includes several existing schemes as special cases. We present  numerical experiments and prove that the linearization gives an  asymptotically consistent solution in the low-Mach limit, a crucial  property for obtaining physically correct solutions.

Speaker : Václav Kučera, associate professor at the Faculty of Mathematics and Physics of Charles University, Prague