Speaker: Remi Abgrall (IMATH & ICS, Zurich)
Title: Some considerations about conservation in the solution of hyperbolic problems
Abstract:
Conservation is a must in many (all) conservation processes. When discretizing a partial differential equation, a rule is to mimic as much as possible the physical principles that has led to the mathematical formulation of the problem. In hyperbolic problems, conservation is a must, and this is the Law since the celebrated theorem of Lax and Wendroff (1960): it provides what should be the generic form of numerical approximation of an hyperbolic problem. On the other hand, the variables that are the 'good' ones to easily translate these physical principles are not necessarily the ones we are interested in: who care about momentum, or total energy? We care about velocity, internal energy and pressure, or temperature.

How far can we depart from the Law, without violating it too much? I will not provide any advise for tax, but some considerations for numerics.