Low Mach number flows: Numerical methods and asymptotic consistency by Václav Kučera

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