It is well known, thanks to Lax-Wendroff theorem, that the local conservation of a numerical scheme for a
conservative hyperbolic system is a simple and systematic way to guarantee that, if stable, a scheme will
provide a sequence of solutions that will converge to a weak solution of the continuous problem. In [1] it is
shown that a nonconservative scheme will not provide a good solution. The
... [Show full abstract] question of using, nevertheless, a
nonconservative formulation of the system and getting the correct solution has been a long-standing debate.
In this paper, we show how to get a relevant weak solution from a pressure-based formulation of the Euler
equations of fluid mechanics. This is useful when dealing with nonlinear equations of state because it is
easier to compute the internal energy from the pressure than the opposite. This makes it possible to get
oscillation-free solutions, contrarily to classical conservative methods. An extension to multiphase flows is
also discussed.