Invited Lecture
Some ideas for large time steps to integrate balance laws
Università di Roma La Sapienza, Italy
Abstract
In recent years we have witnessed a large body of research concentrated on Low Mach problems.
The idea is that in many applications propagation phenomena induced by hyperbolic systems are
characterized by very different speeds, while the phenomenon of interest is carried by low speed waves.
In gas dynamics this typically occurs in almost incompressible flow, where the acoustic waves are much
faster than material waves. In these cases, the classical CFL condition of explicit schemes forces small time steps,
even though one is really interested in the advection of material waves.
In this talk I will describe the issues behind the construction of Low Mach schemes,
and a few solutions on which I have worked. I will consider both intrusive schemes,
exploiting deeply the structure of the equations, and relaxed schemes which promise a more general approach.
I think that this approach is interesting, because most if not all Low Mach schemes are problem-specific.
Applications will be shown to elastic materials and multiphase flows.
Finally, I will conclude with the description of a scheme we are proposing which is
a sort of black box high order implicit scheme for hyperbolic problems.