  Active Flux is an extension of the Finite Volume method and additionally
incorporates point values located at cell boundaries. This gives rise to a
globally continuous approximation of the solution. The method is third-order
accurate. We demonstrate that a new semi-discrete Active Flux method (first
described in Abgrall&Barsukow, 2023 for one space dimension) can easily be used
to solve nonlinear hyperbolic systems in multiple dimensions, such as the
compressible Euler equations of inviscid hydrodynamics. Originally, the Active
Flux method emerged as a fully discrete method, and required an exact or
approximate evolution operator for the point value update. For nonlinear
problems such an operator is often difficult to obtain, in particular for
multiple spatial dimensions. With the new approach it becomes possible to leave
behind these difficulties. We introduce a multi-dimensional limiting strategy
and demonstrate the performance of the new method on both Riemann problems and
subsonic flows.
